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Problems on invariants of knots and 3–manifolds

Tomotada Ohtsuki

Geometry & Topology Monographs 4 (2002) 377–572

DOI: 10.2140/gtm.2002.4.377

Bibliography
1 I Agol, P A Storm, W P Thurston, Lower bounds on volumes of hyperbolic Haken 3–manifolds, J. Amer. Math. Soc. 20 (2007) 1053–1077 MR2328715 With an appendix by Nathan Dunfield
2 H Aida, Unknotting operations of polygonal type, Tokyo J. Math. 15 (1992) 111–121 MR1164189
3 S Akbulut, J D McCarthy, Casson's invariant for oriented homology 3–spheres, Mathematical Notes 36, Princeton University Press (1990) MR1030042 An exposition
4 D Altschuler, Representations of knot groups and Vassiliev invariants, J. Knot Theory Ramifications 5 (1996) 421–425 MR1406713
5 D Altschuler, L Freidel, Vassiliev knot invariants and Chern–Simons perturbation theory to all orders, Comm. Math. Phys. 187 (1997) 261–287 MR1463829
6 J E Andersen, The Witten invariant of finite order mapping tori I, preprint (1995)
7 J E Andersen, G Masbaum, Involutions on moduli spaces and refinements of the Verlinde formula, Math. Ann. 314 (1999) 291–326 MR1697447
8 J E Andersen, J Mattes, N Reshetikhin, The Poisson structure on the moduli space of flat connections and chord diagrams, Topology 35 (1996) 1069–1083 MR1404925
9 J E Andersen, V Turaev, Higher skein modules, J. Knot Theory Ramifications 8 (1999) 963–984 MR1723433
10 J E Andersen, V Turaev, Higher skein modules II, from: "Topology, ergodic theory, real algebraic geometry", Amer. Math. Soc. Transl. Ser. 2 202, Amer. Math. Soc. (2001) 21–30 MR1819178
11 N Andruskiewitsch, M Graña, From racks to pointed Hopf algebras, Adv. Math. 178 (2003) 177–243 MR1994219
12 R P Anstee, J H Przytycki, D Rolfsen, Knot polynomials and generalized mutation, Topology Appl. 32 (1989) 237–249 MR1007103
13 E Appleboim, Finite type invariants of links with a fixed linking matrix, J. Knot Theory Ramifications 11 (2002) 1017–1041 MR1941683
14 M Asaeda, U Haagerup, Exotic subfactors of finite depth with Jones indices (5+\sqrt13)⁄2 and (5+\sqrt17)⁄2, Comm. Math. Phys. 202 (1999) 1–63 MR1686551
15 N Askitas, Multi-#–unknotting operations: a new family of local moves on a knot diagram and related invariants of knots, J. Knot Theory Ramifications 7 (1998) 857–871 MR1654633
16 M Atiyah, Topological quantum field theories, Inst. Hautes Études Sci. Publ. Math. (1988) MR1001453
17 M Atiyah, The geometry and physics of knots, Lezioni Lincee., Cambridge University Press (1990) MR1078014
18 M Atiyah, On framings of 3–manifolds, Topology 29 (1990) 1–7 MR1046621
19 M Atiyah, R Bielawski, Nahm's equations, configuration spaces and flag manifolds, Bull. Braz. Math. Soc. (N.S.) 33 (2002) 157–176 MR1940347
20 M F Atiyah, N Hitchin, R Lawrence, G Segal, Oxford seminar on Jones–Witten theory (1988)
21 S Axelrod, I M Singer, Chern–Simons perturbation theory, from: "Proceedings of the XXth International Conference on Differential Geometric Methods in Theoretical Physics, Vol. 1, 2 (New York, 1991)", World Sci. Publ., River Edge, NJ (1992) 3–45 MR1225107
22 S Axelrod, I M Singer, Chern–Simons perturbation theory II, J. Differential Geom. 39 (1994) 173–213 MR1258919
23 B Bakalov, A Kirillov Jr., Lectures on tensor categories and modular functors, University Lecture Series 21, American Mathematical Society (2001) MR1797619
24 P Bantay, The kernel of the modular representation and the Galois action in RCFT, Comm. Math. Phys. 233 (2003) 423–438 MR1962117
25 D Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995) 423–472 MR1318886
26 D Bar-Natan, Vassiliev homotopy string link invariants, J. Knot Theory Ramifications 4 (1995) 13–32 MR1321289
27 D Bar-Natan, Polynomial invariants are polynomial, Math. Res. Lett. 2 (1995) 239–246 MR1338783
28 D Bar-Natan, Vassiliev and quantum invariants of braids, from: "The interface of knots and physics (San Francisco, CA, 1995)", Proc. Sympos. Appl. Math. 51, Amer. Math. Soc. (1996) 129–144 MR1372767
29 D Bar-Natan, Non-associative tangles, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 139–183 MR1470726
30 D Bar-Natan, On associators and the Grothendieck–Teichmuller group. I, Selecta Math. (N.S.) 4 (1998) 183–212 MR1669949
31 D Bar-Natan, Embedded trivalent graphs and an infant conjecture, talk at the University of California at Berkeley, February 2000
32 D Bar-Natan, On Khovanov's categorification of the Jones polynomial, Algebr. Geom. Topol. 2 (2002) 337–370 MR1917056
33 D Bar-Natan, Web site
34 D Bar-Natan, S Garoufalidis, On the Melvin–Morton–Rozansky conjecture, Invent. Math. 125 (1996) 103–133 MR1389962
35 D Bar-Natan, S Garoufalidis, L Rozansky, D P Thurston, Wheels, wheeling, and the Kontsevich integral of the unknot, Israel J. Math. 119 (2000) 217–237 MR1802655
36 D Bar-Natan, S Garoufalidis, L Rozansky, D P Thurston, The Århus integral of rational homology 3–spheres I: A highly non trivial flat connection on S³, Selecta Math. (N.S.) 8 (2002) 315–339 MR1931167
37 D Bar-Natan, R Lawrence, A rational surgery formula for the LMO invariant, Israel J. Math. 140 (2004) 29–60 MR2054838
38 D Bar-Natan, T T Q Le, D P Thurston, Two applications of elementary knot theory to Lie algebras and Vassiliev invariants, Geom. Topol. 7 (2003) 1–31 MR1988280
39 D Bar-Natan, D P Thurston, Algebraic structures on knotted objects and universal finite type invariants, preprint
40 D Bar-Natan, D P Thurston, Knotted trivalent graphs and their algebra, preprint
41 J W Barrett, B W Westbury, Invariants of piecewise-linear 3–manifolds, Trans. Amer. Math. Soc. 348 (1996) 3997–4022 MR1357878
42 S Baseilhac, Dilogarithm quantique et invariants de 3–variété, thèse de doctorat, Université Paul Sabatier, Toulouse, France (2001)
43 S Baseilhac, R Benedetti, Quantum hyperbolic state sum invariants of 3–manifolds arXiv:math.GT/0101234
44 S Baseilhac, R Benedetti, Bloch-like groups and the volume conjecture revisited, preliminary version (2001)
45 S Baseilhac, R Benedetti, The coloured Jones polynomials from the quantum hyperbolic invariants, in preparation
46 S Baseilhac, R Benedetti, QHI, 3–manifolds scissors congruence classes and the volume conjecture, from: "Invariants of knots and 3–manifolds (Kyoto, 2001)", Geom. Topol. Monogr. 4, Geom. Topol. Publ., Coventry (2002) 13–28 MR2002600
47 A Beliakova, C Blanchet, Modular categories of types B, C and D, Comment. Math. Helv. 76 (2001) 467–500 MR1854694
48 A Beliakova, B Durhuus, On the relation between two quantum group invariants of 3–cobordisms, J. Geom. Phys. 20 (1996) 305–317 MR1419423
49 R Benedetti, C Petronio, Reidemeister–Turaev torsion of 3–dimensional Euler structures with simple boundary tangency and pseudo–Legendrian knots, Manuscripta Math. 106 (2001) 13–61 MR1860979
50 R Benedetti, C Petronio, Combed 3–manifolds with concave boundary, framed links, and pseudo–Legendrian links, J. Knot Theory Ramifications 10 (2001) 1–35 MR1822138
51 S Bigelow, The Burau representation is not faithful for n=5, Geom. Topol. 3 (1999) 397–404 MR1725480
52 S Bigelow, Does the Jones polynomial detect the unknot?, J. Knot Theory Ramifications 11 (2002) 493–505 MR1915491 Knots 2000 Korea, Vol. 2 (Yongpyong)
53 S J Bigelow, Web site
54 S J Bigelow, Braid groups are linear, J. Amer. Math. Soc. 14 (2001) 471–486 MR1815219
55 S Bigelow, A homological definition of the Jones polynomial, from: "Invariants of knots and 3–manifolds (Kyoto, 2001)", Geom. Topol. Monogr. 4, Geom. Topol. Publ., Coventry (2002) 29–41 MR2002601
56 J S Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies 82, Princeton University Press (1974) MR0375281
57 J S Birman, X S Lin, Knot polynomials and Vassiliev's invariants, Invent. Math. 111 (1993) 225–270 MR1198809
58 J S Birman, H Wenzl, Braids, link polynomials and a new algebra, Trans. Amer. Math. Soc. 313 (1989) 249–273 MR992598
59 C Blanchet, A spin decomposition of the Verlinde formulas for type A modular categories, Comm. Math. Phys. 257 (2005) 1–28 MR2163566
60 C Blanchet, N Habegger, G Masbaum, P Vogel, Topological quantum field theories derived from the Kauffman bracket, Topology 34 (1995) 883–927 MR1362791
61 C Blanchet, G Masbaum, Topological quantum field theories for surfaces with spin structure, Duke Math. J. 82 (1996) 229–267 MR1387228
62 J Böckenhauer, D E Evans, Y Kawahigashi, Longo–Rehren subfactors arising from α–induction, Publ. Res. Inst. Math. Sci. 37 (2001) 1–35 MR1815993
63 B Bollobás, O Riordan, Linearized chord diagrams and an upper bound for Vassiliev invariants, J. Knot Theory Ramifications 9 (2000) 847–853 MR1780590
64 F Bonahon, Closed curves on surfaces, book in preparation
65 R Bott, C Taubes, On the self-linking of knots, J. Math. Phys. 35 (1994) 5247–5287 MR1295465 Topology and physics
66 M Brightwell, P Turner, Representations of the homotopy surface category of a simply connected space, J. Knot Theory Ramifications 9 (2000) 855–864 MR1780591
67 D J Broadhurst, Conjectured enumeration of Vassiliev invariants arXiv:q-alg/9709031
68 J F Brock, Weil–Petersson translation distance and volumes of mapping tori, Comm. Anal. Geom. 11 (2003) 987–999 MR2032506
69 D Bullock, The (2,∞)–skein module of the complement of a (2,2p+1) torus knot, J. Knot Theory Ramifications 4 (1995) 619–632 MR1361084
70 D Bullock, On the Kauffman bracket skein module of surgery on a trefoil, Pacific J. Math. 178 (1997) 37–51 MR1447403
71 D Bullock, Rings of SL2(C)–characters and the Kauffman bracket skein module, Comment. Math. Helv. 72 (1997) 521–542 MR1600138
72 D Bullock, A finite set of generators for the Kauffman bracket skein algebra, Math. Z. 231 (1999) 91–101 MR1696758
73 D Bullock, C Frohman, J Kania-Bartoszyńska, Skein homology, Canad. Math. Bull. 41 (1998) 140–144 MR1624157
74 D Bullock, C Frohman, J Kania-Bartoszyńska, Understanding the Kauffman bracket skein module, J. Knot Theory Ramifications 8 (1999) 265–277 MR1691437
75 D Bullock, J H Przytycki, Multiplicative structure of Kauffman bracket skein module quantizations, Proc. Amer. Math. Soc. 128 (2000) 923–931 MR1625701
76 S E Cappell, R Lee, E Y Miller, A symplectic geometry approach to generalized Casson's invariants of 3–manifolds, Bull. Amer. Math. Soc. (N.S.) 22 (1990) 269–275 MR1016041
77 S E Cappell, R Lee, E Y Miller, The action of the Torelli group on the homology of representation spaces is nontrivial, Topology 39 (2000) 851–871 MR1760431
78 J S Carter, M Elhamdadi, M A Nikiforou, M Saito, Extensions of quandles and cocycle knot invariants, J. Knot Theory Ramifications 12 (2003) 725–738 MR2008876
79 J S Carter, D Jelsovsky, S Kamada, L Langford, M Saito, State-sum invariants of knotted curves and surfaces from quandle cohomology, Electron. Res. Announc. Amer. Math. Soc. 5 (1999) 146–156 MR1725613
80 J S Carter, D Jelsovsky, S Kamada, L Langford, M Saito, Quandle cohomology and state-sum invariants of knotted curves and surfaces, Trans. Amer. Math. Soc. 355 (2003) 3947–3989 MR1990571
81 J S Carter, D Jelsovsky, S Kamada, M Saito, Computations of quandle cocycle invariants of knotted curves and surfaces, Adv. Math. 157 (2001) 36–94 MR1808844
82 J S Carter, D Jelsovsky, S Kamada, M Saito, Quandle homology groups, their Betti numbers, and virtual knots, J. Pure Appl. Algebra 157 (2001) 135–155 MR1812049
83 A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Mathematical Society Student Texts 9, Cambridge University Press (1988) MR964685
84 S C Chang, R Shrock, Zeros of Jones polynomials for families of knots and links, Phys. A 301 (2001) 196–218 MR1874776
85 S Chern, J Simons, Some cohomology classes in principal fiber bundles and their application to riemannian geometry, Proc. Nat. Acad. Sci. U.S.A. 68 (1971) 791–794 MR0279732
86 S V Chmutov, S V Duzhin, An upper bound for the number of Vassiliev knot invariants, J. Knot Theory Ramifications 3 (1994) 141–151 MR1279917
87 S Chmutov, S Duzhin, A lower bound for the number of Vassiliev knot invariants, Topology Appl. 92 (1999) 201–223 MR1674810
88 S V Duzhin, A I Kaishev, S V Chmutov, The algebra of 3–graphs, Tr. Mat. Inst. Steklova 221 (1998) 168–196 MR1683693
89 T D Cochran, Derivatives of links: Milnor's concordance invariants and Massey's products, Mem. Amer. Math. Soc. 84 (1990) MR1042041
90 T D Cochran, R E Gompf, Applications of Donaldson's theorems to classical knot concordance, homology 3–spheres and property P, Topology 27 (1988) 495–512 MR976591
91 T D Cochran, P Melvin, Finite type invariants of 3–manifolds, Invent. Math. 140 (2000) 45–100 MR1779798
92 T D Cochran, P Melvin, Quantum cyclotomic orders of 3–manifolds, Topology 40 (2001) 95–125 MR1791269
93 T D Cochran, A Gerges, K Orr, Dehn surgery equivalence relations on 3–manifolds, Math. Proc. Cambridge Philos. Soc. 131 (2001) 97–127 MR1833077
94 J Conant, P Teichner, Grope cobordism of classical knots, Topology 43 (2004) 119–156 MR2030589
95 D Cooper, D D Long, On the Burau representation modulo a small prime, from: "The Epstein birthday schrift", Geom. Topol. Monogr. 1, Geom. Topol. Publ., Coventry (1998) 127–138 MR1668343
96 D Coulson, O A Goodman, C D Hodgson, W D Neumann, Computing arithmetic invariants of 3–manifolds, Experiment. Math. 9 (2000) 127–152 MR1758805
97 P R Cromwell, Homogeneous links, J. London Math. Soc. (2) 39 (1989) 535–552 MR1002465
98 R H Crowell, R H Fox, Introduction to knot theory, Springer (1977) MR0445489 Reprint of the 1963 original, Graduate Texts in Mathematics, No. 57
99 M K Dąbkowski, J H Przytycki, Burnside obstructions to the Montesinos–Nakanishi 3–move conjecture, Geom. Topol. 6 (2002) 355–360 MR1914572
100 O T Dasbach, On the combinatorial structure of primitive Vassiliev invariants II, J. Combin. Theory Ser. A 81 (1998) 127–139 MR1603869
101 O T Dasbach, On the combinatorial structure of primitive Vassiliev invariants III: A lower bound, Commun. Contemp. Math. 2 (2000) 579–590 MR1806948
102 O T Dasbach, S Hougardy, Does the Jones polynomial detect unknottedness?, Experiment. Math. 6 (1997) 51–56 MR1464581
103 O T Dasbach, T D Le, X S Lin, Quantum morphing and the Jones polynomial, Comm. Math. Phys. 224 (2001) 427–442 MR1869873
104 J Dean, Many classical knot invariants are not Vassiliev invariants, J. Knot Theory Ramifications 3 (1994) 7–10 MR1265449
105 C De Concini, C Procesi, Quantum groups, from: "D–modules, representation theory, and quantum groups (Venice, 1992)", Lecture Notes in Math. 1565, Springer (1993) 31–140 MR1288995
106 F Deloup, On abelian quantum invariants of links in 3–manifolds, Math. Ann. 319 (2001) 759–795 MR1825407
107 F Deloup, G Massuyeau, Quadratic functions and complex spin structures on three-manifolds, Topology 44 (2005) 509–555 MR2122215
108 R Dijkgraaf, E Witten, Topological gauge theories and group cohomology, Comm. Math. Phys. 129 (1990) 393–429 MR1048699
109 I Dogolazky, Eine Abhandlung über die Algebra der Schlingeldiagramme, thesis, Universität Bonn (1998)
110 S K Donaldson, Topological field theories and formulae of Casson and Meng–Taubes, from: "Proceedings of the Kirbyfest (Berkeley, CA, 1998)", Geom. Topol. Monogr. 2, Geom. Topol. Publ., Coventry (1999) 87–102 MR1734402
111 V G Drinfel'd, Quantum groups, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986)", Amer. Math. Soc. (1987) 798–820 MR934283
112 N Dunfield, Web site
113 D Eisenbud, Commutative algebra, Graduate Texts in Mathematics 150, Springer (1995) MR1322960 With a view toward algebraic geometry
114 M Eisermann, The number of knot group representations is not a Vassiliev invariant, Proc. Amer. Math. Soc. 128 (2000) 1555–1561 MR1657727
115 S Eliahou, L H Kauffman, M B Thistlethwaite, Infinite families of links with trivial Jones polynomial, Topology 42 (2003) 155–169 MR1928648
116 P Etingof, A Soloviev, R Guralnick, Indecomposable set-theoretical solutions to the quantum Yang–Baxter equation on a set with a prime number of elements, J. Algebra 242 (2001) 709–719 MR1848966
117 P Etingof, D Kazhdan, Quantization of Lie bialgebras I, Selecta Math. (N.S.) 2 (1996) 1–41 MR1403351
118 D E Evans, Y Kawahigashi, Quantum symmetries on operator algebras, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press (1998) MR1642584 Oxford Science Publications
119 G Everest, Measuring the height of a polynomial, Math. Intelligencer 20 (1998) 9–16 MR1646573
120 L D Faddeev, R M Kashaev, Quantum dilogarithm, Modern Phys. Lett. A 9 (1994) 427–434 MR1264393
121 R Fenn, C Rourke, Racks and links in codimension two, J. Knot Theory Ramifications 1 (1992) 343–406 MR1194995
122 R Fenn, C Rourke, B Sanderson, An introduction to species and the rack space, from: "Topics in knot theory (Erzurum, 1992)", NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 399, Kluwer Acad. Publ. (1993) 33–55 MR1257904
123 R Fenn, C Rourke, B Sanderson, James bundles, Proc. London Math. Soc. (3) 89 (2004) 217–240 MR2063665
124 R Fenn, C Rourke, B Sanderson, The rack space, Trans. Amer. Math. Soc. 359 (2007) 701–740 MR2255194
125 E Ferrand, On Legendrian knots and polynomial invariants, Proc. Amer. Math. Soc. 130 (2002) 1169–1176 MR1873793
126 E Formanek, Braid group representations of low degree, Proc. London Math. Soc. (3) 73 (1996) 279–322 MR1397691
127 D S Freed, R E Gompf, Computer calculation of Witten's 3–manifold invariant, Comm. Math. Phys. 141 (1991) 79–117 MR1133261
128 C Frohman, A Nicas, The Alexander polynomial via topological quantum field theory, from: "Differential geometry, global analysis, and topology (Halifax, NS, 1990)", CMS Conf. Proc. 12, Amer. Math. Soc. (1991) 27–40 MR1158467
129 C Frohman, A Nicas, An intersection homology invariant for knots in a rational homology 3–sphere, Topology 33 (1994) 123–158 MR1259519
130 D Fuchs, S Tabachnikov, Invariants of Legendrian and transverse knots in the standard contact space, Topology 36 (1997) 1025–1053 MR1445553
131 S Fukuhara, Y Matsumoto, K Sakamoto, Casson's invariant of Seifert homology 3–spheres, Math. Ann. 287 (1990) 275–285 MR1054569
132 L Funar, On the TQFT representations of the mapping class groups, Pacific J. Math. 188 (1999) 251–274 MR1684208
133 D Gabai, Foliations and genera of links, Topology 23 (1984) 381–394 MR780731
134 S Garoufalidis, Relations among 3–manifold invariants, thesis, Chicago University (1992)
135 S Garoufalidis, On finite type 3–manifold invariants I, J. Knot Theory Ramifications 5 (1996) 441–461 MR1406715
136 S Garoufalidis, Applications of quantum invariants in low-dimensional topology, Topology 37 (1998) 219–224 MR1480887
137 S Garoufalidis, M Goussarov, M Polyak, Calculus of clovers and finite type invariants of 3–manifolds, Geom. Topol. 5 (2001) 75–108 MR1812435
138 S Garoufalidis, N Habegger, The Alexander polynomial and finite type 3–manifold invariants, Math. Ann. 316 (2000) 485–497 MR1752781
139 S Garoufalidis, A Kricker, A rational noncommutative invariant of boundary links, Geom. Topol. 8 (2004) 115–204 MR2033481
140 S Garoufalidis, J Levine, Finite type 3–manifold invariants, the mapping class group and blinks, J. Differential Geom. 47 (1997) 257–320 MR1601612
141 S Garoufalidis, T Ohtsuki, On finite type 3–manifold invariants III: Manifold weight systems, Topology 37 (1998) 227–243 MR1489202
142 S Garoufalidis, L Rozansky, The loop expansion of the Kontsevich integral, the null-move and S–equivalence, Topology 43 (2004) 1183–1210 MR2080000
143 P M Gilmer, Invariants for one-dimensional cohomology classes arising from TQFT, Topology Appl. 75 (1997) 217–259 MR1430088
144 P M Gilmer, On the Witten–Reshetikhin–Turaev representations of mapping class groups, Proc. Amer. Math. Soc. 127 (1999) 2483–2488 MR1487369
145 P M Gilmer, Integrality for TQFTs, Duke Math. J. 125 (2004) 389–413 MR2096678
146 P M Gilmer, J K Zhong, On the Homflypt skein module of S¹× S², Math. Z. 237 (2001) 769–814 MR1854090
147 P M Gilmer, J K Zhong, The Homflypt skein module of a connected sum of 3–manifolds, Algebr. Geom. Topol. 1 (2001) 605–625 MR1875610
148 F M Goodman, P de la Harpe, V F R Jones, Coxeter graphs and towers of algebras, Mathematical Sciences Research Institute Publications 14, Springer (1989) MR999799
149 R Gopakumar, C Vafa, Topological gravity as large N topological gauge theory, Adv. Theor. Math. Phys. 2 (1998) 413–442 MR1633024
150 M N Goussarov, A new form of the Conway–Jones polynomial of oriented links, from: "Topology of manifolds and varieties" (editor O Viro), Adv. Soviet Math. 18, Amer. Math. Soc. (1994) 167–172 MR1296894
151 M N Goussarov, On n–equivalence of knots and invariants of finite degree, from: "Topology of manifolds and varieties", Adv. Soviet Math. 18, Amer. Math. Soc. (1994) 173–192 MR1296895
152 M N Goussarov, Knotted graphs and a geometrical technique of n–equivalence, POMI Saint Petersburg preprint (1995)
153 M Goussarov, Finite type invariants and n–equivalence of 3–manifolds, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 517–522 MR1715131
154 M Goussarov, M Polyak, O Viro, Finite-type invariants of classical and virtual knots, Topology 39 (2000) 1045–1068 MR1763963
155 M Graña, Quandle knot invariants are quantum knot invariants, J. Knot Theory Ramifications 11 (2002) 673–681 MR1918807
156 M Graña, Indecomposable racks of order p², Beiträge Algebra Geom. 45 (2004) 665–676 MR2093034
157 H Gruber, Estimates for the minimal crossing number arXiv:math.GT/0303273
158 E Guadagnini, L Pilo, Three-manifold invariants and their relation with the fundamental group, Comm. Math. Phys. 192 (1998) 47–65 MR1612144
159 L Guillou, A Marin, Notes sur l'invariant de Casson des sphères d'homologie de dimension trois, Enseign. Math. (2) 38 (1992) 233–290 MR1189008 With an appendix by Christine Lescop
160 U Haagerup, Principal graphs of subfactors in the index range 4<[M:N]<3+\sqrt2, from: "Subfactors (Kyuzeso, 1993)", World Sci. Publ., River Edge, NJ (1994) 1–38 MR1317352
161 N Habegger, A computation of the universal quantum 3–manifold invariant for manifolds of rank greater than 2, preprint (1996)
162 N Habegger, A Beliakova, The Casson–Walker–Lescop invariant as a quantum 3–manifold invariant, J. Knot Theory Ramifications 9 (2000) 459–470 MR1758865
163 N Habegger, X S Lin, The classification of links up to link-homotopy, J. Amer. Math. Soc. 3 (1990) 389–419 MR1026062
164 N Habegger, G Masbaum, The Kontsevich integral and Milnor's invariants, Topology 39 (2000) 1253–1289 MR1783857
165 K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1–83 MR1735632
166 K Habiro, On the quantum sl2 invariants of knots and integral homology spheres, from: "Invariants of knots and 3–manifolds (Kyoto, 2001)", Geom. Topol. Monogr. 4, Geom. Topol. Publ., Coventry (2002) 55–68 MR2002603
167 K Habiro, T T Q Le, in preparation
168 S K Hansen, Reshetikhin–Turaev invariants of Seifert 3–manifolds, and their asymptotic expansions, PhD thesis, Aarhus University (1999)
169 T Harikae, Y Uchida, Irregular dihedral branched coverings of knots, from: "Topics in knot theory (Erzurum, 1992)", NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 399, Kluwer Acad. Publ. (1993) 269–276 MR1257914
170 R Hartley, A Kawauchi, Polynomials of amphicheiral knots, Math. Ann. 243 (1979) 63–70 MR543095
171 A Hatcher, Spaces of knots arXiv:math.GT/9909095
172 N Hitchin, Lie groups and Teichmüller space, Topology 31 (1992) 449–473 MR1174252
173 N Hitchin, J Sawon, Curvature and characteristic numbers of hyper–Kähler manifolds, Duke Math. J. 106 (2001) 599–615 MR1813238
174 J Hoste, M E Kidwell, Dichromatic link invariants, Trans. Amer. Math. Soc. 321 (1990) 197–229 MR961623
175 J Hoste, J H Przytycki, An invariant of dichromatic links, Proc. Amer. Math. Soc. 105 (1989) 1003–1007 MR989100
176 J Hoste, J H Przytycki, Homotopy skein modules of orientable 3–manifolds, Math. Proc. Cambridge Philos. Soc. 108 (1990) 475–488 MR1068450
177 J Hoste, J H Przytycki, A survey of skein modules of 3–manifolds, from: "Knots 90 (Osaka, 1990)", de Gruyter (1992) 363–379 MR1177433
178 J Hoste, J H Przytycki, The (2,∞)–skein module of lens spaces; a generalization of the Jones polynomial, J. Knot Theory Ramifications 2 (1993) 321–333 MR1238877
179 J Hoste, J H Przytycki, The Kauffman bracket skein module of S¹×S², Math. Z. 220 (1995) 65–73 MR1347158
180 J Hoste, J H Przytycki, The (2,∞)–skein module of Whitehead manifolds, J. Knot Theory Ramifications 4 (1995) 411–427 MR1347362
181 J Hoste, M Thistlethwaite, J Weeks, The first 1,701,936 knots, Math. Intelligencer 20 (1998) 33–48 MR1646740
182 A Inoue, Quandle homomorphisms of knot quandles to Alexander quandles, J. Knot Theory Ramifications 10 (2001) 813–821 MR1840269
183 M Izumi, The structure of sectors associated with Longo–Rehren inclusions I: General theory, Comm. Math. Phys. 213 (2000) 127–179 MR1782145
184 F Jaeger, D L Vertigan, D J A Welsh, On the computational complexity of the Jones and Tutte polynomials, Math. Proc. Cambridge Philos. Soc. 108 (1990) 35–53 MR1049758
185 L C Jeffrey, Chern–Simons–Witten invariants of lens spaces and torus bundles, and the semiclassical approximation, Comm. Math. Phys. 147 (1992) 563–604 MR1175494
186 D Jelsovsky, M Saito, Maple programs for computing quandle cohomology and cocycle knot invariants
187 V F R Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. (N.S.) 12 (1985) 103–111 MR766964
188 V F R Jones, Actions of discrete groups on factors, from: "Operator algebras and applications, Part 2 (Kingston, Ont., 1980)", Proc. Sympos. Pure Math. 38, Amer. Math. Soc. (1982) 167–177 MR679504
189 V F R Jones, Ten problems, from: "Mathematics: frontiers and perspectives", Amer. Math. Soc. (2000) 79–91 MR1754769
190 V F R Jones, D P O Rolfsen, A theorem regarding 4–braids and the V=1 problem, from: "Proceedings of the Conference on Quantum Topology (Manhattan, KS, 1993)", World Sci. Publ., River Edge, NJ (1994) 127–135 MR1309931
191 D Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982) 37–65 MR638121
192 U Kaiser, Presentations of homotopy skein modules of oriented 3–manifolds, J. Knot Theory Ramifications 10 (2001) 461–491 MR1825969
193 T Kanenobu, Infinitely many knots with the same polynomial invariant, Proc. Amer. Math. Soc. 97 (1986) 158–162 MR831406
194 J Kania-Bartoszyńska, J H Przytycki, A S Sikora, Estimating the size of skein homologies, from: "Knots in Hellas '98 (Delphi)", Ser. Knots Everything 24, World Sci. Publ., River Edge, NJ (2000) 138–142 MR1865706
195 M Kapranov, Rozansky–Witten invariants via Atiyah classes, Compositio Math. 115 (1999) 71–113 MR1671737
196 R M Kashaev, Quantum dilogarithm as a 6j–symbol, Modern Phys. Lett. A 9 (1994) 3757–3768 MR1317945
197 R M Kashaev, A link invariant from quantum dilogarithm, Modern Phys. Lett. A 10 (1995) 1409–1418 MR1341338
198 R M Kashaev, The algebraic nature of quantum dilogarithm, from: "Geometry and integrable models (Dubna, 1994)", World Sci. Publ., River Edge, NJ (1996) 32–51 MR1413505
199 R M Kashaev, The hyperbolic volume of knots from the quantum dilogarithm, Lett. Math. Phys. 39 (1997) 269–275 MR1434238
200 R M Kashaev, Quantum hyperbolic invariants of knots, from: "Discrete integrable geometry and physics (Vienna, 1996)", Oxford Lecture Ser. Math. Appl. 16, Oxford Univ. Press (1999) 343–359 MR1676604
201 R M Kashaev, O Tirkkonen, A proof of the volume conjecture on torus knots, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 269 (2000) 262–268, 370 MR1805865
202 C Kassel, Quantum groups, Graduate Texts in Mathematics 155, Springer (1995) MR1321145
203 L H Kauffman, Formal knot theory, Mathematical Notes 30, Princeton University Press (1983) MR712133
204 L H Kauffman, Virtual knot theory, European J. Combin. 20 (1999) 663–690 MR1721925
205 Y Kawahigashi, N Sato, M Wakui, (2+1)–dimensional topological quantum field theory from subfactors and Dehn surgery formula for 3–manifold invariants, Adv. Math. 195 (2005) 165–204 MR2145795
206 A Kawauchi, Topological imitation, mutation and the quantum \mathrm SU(2) invariants, J. Knot Theory Ramifications 3 (1994) 25–39 MR1265451
207 A Kawauchi, A survey of knot theory, Birkhäuser Verlag (1996) MR1417494 Translated and revised from the 1990 Japanese original by the author
208 A Kawauchi, S Kojima, Algebraic classification of linking pairings on 3–manifolds, Math. Ann. 253 (1980) 29–42 MR594531
209 T Kerler, Non–Tannakian categories in quantum field theory, from: "New symmetry principles in quantum field theory (Cargèse, 1991)", NATO Adv. Sci. Inst. Ser. B Phys. 295, Plenum (1992) 449–482 MR1204468
210 T Kerler, Genealogy of non-perturbative quantum-invariants of 3–manifolds: the surgical family, from: "Geometry and physics (Aarhus, 1995)", Lecture Notes in Pure and Appl. Math. 184, Dekker (1997) 503–547 MR1423190
211 T Kerler, On the connectivity of cobordisms and half-projective TQFT's, Comm. Math. Phys. 198 (1998) 535–590 MR1670025
212 T Kerler, Resolutions of p–modular TQFTs and representations of symmetric groups arXiv:math.GT/0110006
213 T Kerler, p–modular TQFT's, Milnor torsion and the Casson–Lescop invariant, from: "Invariants of knots and 3–manifolds (Kyoto, 2001)", Geom. Topol. Monogr. 4, Geom. Topol. Publ., Coventry (2002) 119–141 MR2002607
214 T Kerler, On the structure of the Fibonacci TQFT, in final preparation
215 T Kerler, Homology TQFT's and the Alexander–Reidemeister invariant of 3–manifolds via Hopf algebras and skein theory, Canad. J. Math. 55 (2003) 766–821 MR1994073
216 T Kerler, Towards an algebraic characterization of 3–dimensional cobordisms, from: "Diagrammatic morphisms and applications (San Francisco, CA, 2000)", Contemp. Math. 318, Amer. Math. Soc. (2003) 141–173 MR1973515
217 T Kerler, V V Lyubashenko, Non-semisimple topological quantum field theories for 3–manifolds with corners, Lecture Notes in Mathematics 1765, Springer (2001) MR1862634
218 M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359–426 MR1740682
219 M Khovanov, A functor-valued invariant of tangles, Algebr. Geom. Topol. 2 (2002) 665–741 MR1928174
220 M Khovanov, G Kuperberg, Web bases for sl(3) are not dual canonical, Pacific J. Math. 188 (1999) 129–153 MR1680395
221 , Problems in low-dimensional topology, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35–473 MR1470751 Edited by Rob Kirby
222 R Kirby, P Melvin, The 3–manifold invariants of Witten and Reshetikhin–Turaev for sl(2,C), Invent. Math. 105 (1991) 473–545 MR1117149
223 A Kirillov Jr., V Ostrik, On a q–analogue of the McKay correspondence and the ADE classification of sl2 conformal field theories, Adv. Math. 171 (2002) 183–227 MR1936496
224 P Kirk, C Livingston, Vassiliev invariants of two component links and the Casson–Walker invariant, Topology 36 (1997) 1333–1353 MR1452854
225 J A Kneissler, The number of primitive Vassiliev invariants up to degree 12 arXiv:q-alg/9706022
226 M Kontsevich, Vassiliev's knot invariants, from: "I. M. Gel'fand Seminar", Adv. Soviet Math. 16, Amer. Math. Soc. (1993) 137–150 MR1237836
227 M Kontsevich, Feynman diagrams and low-dimensional topology, from: "First European Congress of Mathematics, Vol. II (Paris, 1992)", Progr. Math. 120, Birkhäuser (1994) 97–121 MR1341841
228 M Kontsevich, Rozansky–Witten invariants via formal geometry, Compositio Math. 115 (1999) 115–127 MR1671725
229 S Kojima, S Negami, Teijigen topology to sono shuuhen (Low dimensional topology and related topics), unpublished problem list (1987)
230 D Krammer, Braid groups are linear, Ann. of Math. (2) 155 (2002) 131–156 MR1888796
231 A Kricker, Covering spaces over claspered knots arXiv:math.GT/9901029
232 A Kricker, The lines of the Kontsevich integral and Rozansky's rationality conjecture arXiv:math.GT/0005284
233 A Kricker, Branched cyclic covers and finite type invariants, J. Knot Theory Ramifications 12 (2003) 135–158 MR1967238
234 G Kuperberg, The quantum G2 link invariant, Internat. J. Math. 5 (1994) 61–85 MR1265145
235 G Kuperberg, Spiders for rank 2 Lie algebras, Comm. Math. Phys. 180 (1996) 109–151 MR1403861
236 G Kuperberg, Detecting knot invertibility, J. Knot Theory Ramifications 5 (1996) 173–181 MR1395778
237 G Kuperberg, Noninvolutory Hopf algebras and 3–manifold invariants, Duke Math. J. 84 (1996) 83–129 MR1394749
238 G Kuperberg, D P Thurston, Perturbative 3–manifold invariants by cut-and-paste topology arXiv:math.GT/9912167
239 M Lackenby, The volume of hyperbolic alternating link complements, Proc. London Math. Soc. (3) 88 (2004) 204–224 MR2018964 With an appendix by Ian Agol and Dylan Thurston
240 R J Lawrence, Asymptotic expansions of Witten–Reshetikhin–Turaev invariants for some simple 3–manifolds, J. Math. Phys. 36 (1995) 6106–6129 MR1355900
241 R J Lawrence, Braid group representations associated with slm, J. Knot Theory Ramifications 5 (1996) 637–660 MR1414092
242 R J Lawrence, Witten–Reshetikhin–Turaev invariants of 3–manifolds as holomorphic functions, from: "Geometry and physics (Aarhus, 1995)", Lecture Notes in Pure and Appl. Math. 184, Dekker (1997) 363–377 MR1423181
243 R Lawrence, L Rozansky, Witten–Reshetikhin–Turaev invariants of Seifert manifolds, Comm. Math. Phys. 205 (1999) 287–314 MR1712599
244 R Lawrence, D Zagier, Modular forms and quantum invariants of 3–manifolds, Asian J. Math. 3 (1999) 93–107 MR1701924 Sir Michael Atiyah: a great mathematician of the twentieth century
245 T T Q Le, An invariant of integral homology 3–spheres which is universal for all finite type invariants, from: "Solitons, geometry, and topology: on the crossroad", Amer. Math. Soc. Transl. Ser. 2 179, Amer. Math. Soc. (1997) 75–100 MR1437158
246 T T Q Le, On perturbative PSU(n) invariants of rational homology 3–spheres, Topology 39 (2000) 813–849 MR1760430
247 T T Q Le, Integrality and symmetry of quantum link invariants, Duke Math. J. 102 (2000) 273–306 MR1749439
248 T T Q Le, Quantum invariants of 3–manifolds: integrality, splitting, and perturbative expansion, from: "Proceedings of the Pacific Institute for the Mathematical Sciences Workshop “Invariants of Three–Manifolds” (Calgary, AB, 1999)" (2003) 125–152 MR1953323
249 T Q T Le, J Murakami, Kontsevich's integral for the Homfly polynomial and relations between values of multiple zeta functions, Topology Appl. 62 (1995) 193–206 MR1320252
250 T T Q Le, J Murakami, T Ohtsuki, On a universal perturbative invariant of 3–manifolds, Topology 37 (1998) 539–574 MR1604883
251 T Le, V Turaev, Quantum groups and ribbon G–categories, J. Pure Appl. Algebra 178 (2003) 169–185 MR1952424
252 C Lescop, Global surgery formula for the Casson–Walker invariant, Annals of Mathematics Studies 140, Princeton University Press (1996) MR1372947
253 C Lescop, About the uniqueness of the Kontsevich integral, J. Knot Theory Ramifications 11 (2002) 759–780 MR1918812
254 J Levine, A method for generating link polynomials, Amer. J. Math. 89 (1967) 69–84 MR0224082
255 J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229–244 MR0246314
256 W B R Lickorish, An introduction to knot theory, Graduate Texts in Mathematics 175, Springer (1997) MR1472978
257 W B R Lickorish, Sampling the SU(N) invariants of three-manifolds, J. Knot Theory Ramifications 6 (1997) 45–60 MR1442179
258 W B R Lickorish, K C Millett, Some evaluations of link polynomials, Comment. Math. Helv. 61 (1986) 349–359 MR860127
259 W B R Lickorish, Y Rong, On derivatives of link polynomials, Topology Appl. 87 (1998) 63–71 MR1626084
260 J Lieberum, The LMO-invariant of 3–manifolds of rank one and the Alexander polynomial, Math. Ann. 318 (2000) 761–776 MR1802509
261 J Lieberum, Skein modules of links in cylinders over surfaces, Int. J. Math. Math. Sci. 32 (2002) 515–554 MR1951085
262 X S Lin, Power series expansions and invariants of links, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 184–202 MR1470727
263 X S Lin, Web site
264 X S Lin, Z Wang, Integral geometry of plane curves and knot invariants, J. Differential Geom. 44 (1996) 74–95 MR1420350
265 R A Litherland, S Nelson, The Betti numbers of some finite racks, J. Pure Appl. Algebra 178 (2003) 187–202 MR1952425
266 C Livingston, Knots which are not concordant to their reverses, Quart. J. Math. Oxford Ser. (2) 34 (1983) 323–328 MR711524
267 C Livingston, The slicing number of a knot, Algebr. Geom. Topol. 2 (2002) 1051–1060 MR1936979
268 W F Lofaro, A Mayer–Vietoris theorem for the Kauffman bracket skein module, J. Knot Theory Ramifications 8 (1999) 721–729 MR1708008
269 D D Long, A note on the normal subgroups of mapping class groups, Math. Proc. Cambridge Philos. Soc. 99 (1986) 79–87 MR809501
270 D D Long, M Paton, The Burau representation is not faithful for n≥ 6, Topology 32 (1993) 439–447 MR1217079
271 J Marché, On Kontsevich integral of torus knots, Topology Appl. 143 (2004) 15–26 MR2080280
272 M Marcolli, Seiberg–Witten gauge theory, Texts and Readings in Mathematics 17, Hindustan Book Agency (1999) MR1700273 With an appendix by the author and Erion J. Clark
273 B Martelli, C Petronio, Three-manifolds having complexity at most 9, Experiment. Math. 10 (2001) 207–236 MR1837672
274 B Martelli, C Petronio, A new decomposition theorem for 3–manifolds, Illinois J. Math. 46 (2002) 755–780 MR1951239
275 G Masbaum, An element of infinite order in TQFT-representations of mapping class groups, from: "Low-dimensional topology (Funchal, 1998)", Contemp. Math. 233, Amer. Math. Soc. (1999) 137–139 MR1701678
276 G Masbaum, J D Roberts, On central extensions of mapping class groups, Math. Ann. 302 (1995) 131–150 MR1329450
277 G Massuyeau, Spin Borromean surgeries, Trans. Amer. Math. Soc. 355 (2003) 3991–4017 MR1990572
278 S V Matveev, Distributive groupoids in knot theory, Mat. Sb. (N.S.) 119(161) (1982) 78–88, 160 MR672410
279 S V Matveev, Generalized surgeries of three-dimensional manifolds and representations of homology spheres, Mat. Zametki 42 (1987) 268–278, 345 MR915115
280 S V Matveev, Complexity theory of three-dimensional manifolds, Acta Appl. Math. 19 (1990) 101–130 MR1074221
281 B Mellor, Finite type link homotopy invariants II: Milnor's $µ–invariants, J. Knot Theory Ramifications 9 (2000) 735–758 MR1775384
282 W Menasco, M Thistlethwaite, The classification of alternating links, Ann. of Math. (2) 138 (1993) 113–171 MR1230928
283 R Meyerhoff, Hyperbolic 3–manifolds with equal volumes but different Chern–Simons invariants, from: "Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984)", London Math. Soc. Lecture Note Ser. 112, Cambridge Univ. Press (1986) 209–215 MR903866
284 J Milnor, Link groups, Ann. of Math. (2) 59 (1954) 177–195 MR0071020
285 T Mochizuki, Some calculations of cohomology groups of finite Alexander quandles, J. Pure Appl. Algebra 179 (2003) 287–330 MR1960136
286 H R Morton, Problems, from: "Braids (Santa Cruz, CA, 1986)", Contemp. Math. 78, Amer. Math. Soc. (1988) 557–574 MR975094
287 , Problems, from: "Knots in Hellas '98 (Delphi)", Ser. Knots Everything 24, World Sci. Publ., River Edge, NJ (2000) 547–559 MR1865730 Edited by H. R. Morton
288 J Mostovoy, Short ropes and long knots, Topology 41 (2002) 435–450 MR1910036
289 M Müger, Galois theory for braided tensor categories and the modular closure, Adv. Math. 150 (2000) 151–201 MR1749250
290 H Murakami, Some metrics on classical knots, Math. Ann. 270 (1985) 35–45 MR769605
291 H Murakami, A recursive calculation of the Arf invariant of a link, J. Math. Soc. Japan 38 (1986) 335–338 MR833206
292 H Murakami, Quantum SO(3)–invariants dominate the SU(2)–invariant of Casson and Walker, Math. Proc. Cambridge Philos. Soc. 117 (1995) 237–249 MR1307078
293 H Murakami, Quantum SU(2)–invariants of three-manifolds associated with the trivial first cohomology class modulo two, from: "Low-dimensional topology (Funchal, 1998)", Contemp. Math. 233, Amer. Math. Soc. (1999) 117–136 MR1701677
294 H Murakami, Quantum SU(2)–invariants for three-manifolds associated with non-trivial cohomology classes modulo two, from: "Knots in Hellas '98 (Delphi)", Ser. Knots Everything 24, World Sci. Publ., River Edge, NJ (2000) 347–352 MR1865716
295 H Murakami, Optimistic calculations about the Witten–Reshetikhin–Turaev invariants of closed three-manifolds obtained from the figure-eight knot by integral Dehn surgeries, Sūrikaisekikenkyūsho Kōkyūroku (2000) 70–79 MR1805729 Recent progress towards the volume conjecture (Japanese) (Kyoto, 2000)
296 H Murakami, Kashaev's invariant and the volume of a hyperbolic knot after Y. Yokota, from: "Physics and combinatorics 1999 (Nagoya)", World Sci. Publ., River Edge, NJ (2001) 244–272 MR1865040
297 H Murakami, J Murakami, The colored Jones polynomials and the simplicial volume of a knot, Acta Math. 186 (2001) 85–104 MR1828373
298 H Murakami, J Murakami, M Okamoto, T Takata, Y Yokota, Kashaev's conjecture and the Chern–Simons invariants of knots and links, Experiment. Math. 11 (2002) 427–435 MR1959752
299 H Murakami, Y Nakanishi, On a certain move generating link-homology, Math. Ann. 284 (1989) 75–89 MR995383
300 H Murakami, T Ohtsuki, Finite type invariants of knots via their Seifert matrices, Asian J. Math. 5 (2001) 379–386 MR1868640
301 J Murakami, The Kauffman polynomial of links and representation theory, Osaka J. Math. 24 (1987) 745–758 MR927059
302 J Murakami, T Ohtsuki, Topological quantum field theory for the universal quantum invariant, Comm. Math. Phys. 188 (1997) 501–520 MR1473309
303 J Murakami, M Yano, On the volume of a hyperbolic and spherical tetrahedron, Comm. Anal. Geom. 13 (2005) 379–400 MR2154824
304 K Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965) 387–422 MR0171275
305 S Naik, T Stanford, A move on diagrams that generates S–equivalence of knots, J. Knot Theory Ramifications 12 (2003) 717–724 MR1999640
306 Y Nakanishi, On generalized unknotting operations, J. Knot Theory Ramifications 3 (1994) 197–209 MR1279922
307 Y Nakanishi, Delta link homotopy for two component links, from: "Proceedings of the First Joint Japan–Mexico Meeting in Topology (Morelia, 1999)" (2002) 169–182 MR1903689
308 Y Nakanishi, Y Ohyama, Delta link homotopy for two component links III, J. Math. Soc. Japan 55 (2003) 641–654 MR1978214
309 S Nelson, Classification of finite Alexander quandles, from: "Proceedings of the Spring Topology and Dynamical Systems Conference" (2003) 245–258 MR2048935
310 W D Neumann, Combinatorics of triangulations and the Chern–Simons invariant for hyperbolic 3–manifolds, from: "Topology '90 (Columbus, OH, 1990)", Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 243–271 MR1184415
311 W D Neumann, Hilbert's 3rd problem and invariants of 3–manifolds, from: "The Epstein birthday schrift", Geom. Topol. Monogr. 1, Geom. Topol. Publ., Coventry (1998) 383–411 MR1668316
312 W D Neumann, D Zagier, Volumes of hyperbolic three-manifolds, Topology 24 (1985) 307–332 MR815482
313 K Y Ng, Groups of ribbon knots, Topology 37 (1998) 441–458 MR1489214
314 K Y Ng, T Stanford, On Gusarov's groups of knots, Math. Proc. Cambridge Philos. Soc. 126 (1999) 63–76 MR1681654
315 D Nikshych, V Turaev, L Vainerman, Invariants of knots and 3–manifolds from quantum groupoids, from: "Proceedings of the Pacific Institute for the Mathematical Sciences Workshop “Invariants of Three–Manifolds” (Calgary, AB, 1999)" (2003) 91–123 MR1953322
316 A Ocneanu, Chirality for operator algebras, from: "Subfactors (Kyuzeso, 1993)", World Sci. Publ., River Edge, NJ (1994) 39–63 MR1317353
317 A Ocneanu, Operator algebras, topology and subgroups of quantum symmetry—construction of subgroups of quantum groups, from: "Taniguchi Conference on Mathematics Nara '98", Adv. Stud. Pure Math. 31, Math. Soc. Japan (2001) 235–263 MR1865095
318 A M Odlyzko, B Poonen, Zeros of polynomials with 0,1 coefficients, Enseign. Math. (2) 39 (1993) 317–348 MR1252071
319 T Ohtsuki, Finite type invariants of integral homology 3–spheres, J. Knot Theory Ramifications 5 (1996) 101–115 MR1373813
320 T Ohtsuki, A polynomial invariant of rational homology 3–spheres, Invent. Math. 123 (1996) 241–257 MR1374199
321 T Ohtsuki, The perturbative SO(3) invariant of rational homology 3–spheres recovers from the universal perturbative invariant, Topology 39 (2000) 1103–1135 MR1783850
322 T Ohtsuki, Quantum invariants, Series on Knots and Everything 29, World Scientific Publishing Co. (2002) MR1881401 A study of knots, 3–manifolds, and their sets
323 T Ohtsuki, A cabling formula for the 2–loop polynomial of knots, Publ. Res. Inst. Math. Sci. 40 (2004) 949–971 MR2074706
324 T Ohtsuki, S Yamada, Quantum SU(3) invariant of 3–manifolds via linear skein theory, J. Knot Theory Ramifications 6 (1997) 373–404 MR1457194
325 Y Ohyama, Vassiliev invariants and similarity of knots, Proc. Amer. Math. Soc. 123 (1995) 287–291 MR1234630
326 N Okuda, On the first two Vassiliev invariants of some sequences of knots, in Japanese, master's thesis, Tokyo Institute of Technology (2002)
327 P Ozsváth, Z Szabó, The theta divisor and the Casson–Walker invariant arXiv:math.GT/0006194
328 R C Penner, J L Harer, Combinatorics of train tracks, Annals of Mathematics Studies 125, Princeton University Press (1992) MR1144770
329 S Poirier, The configuration space integral for links in R³, Algebr. Geom. Topol. 2 (2002) 1001–1050 MR1936978
330 M Polyak, Skein relations for Milnor's µ–invariants, Algebr. Geom. Topol. 5 (2005) 1471–1479 MR2186105
331 M Polyak, On the algebra of arrow diagrams, Lett. Math. Phys. 51 (2000) 275–291 MR1778064
332 M Polyak, O Viro, On the Casson knot invariant, J. Knot Theory Ramifications 10 (2001) 711–738 MR1839698 Knots in Hellas '98, Vol. 3 (Delphi)
333 G Ponzano, T Regge, Semi-classical limit of Racah coefficients, from: "Spectroscopic and group theoretical methods in physics" (editor F Bloch), North-Holland (1968) 1–58
334 J H Przytycki, Skein modules of 3–manifolds, Bull. Polish Acad. Sci. Math. 39 (1991) 91–100 MR1194712
335 J H Przytycki, Skein module of links in a handlebody, from: "Topology '90 (Columbus, OH, 1990)", Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 315–342 MR1184418
336 J H Przytycki, Quantum group of links in a handlebody, from: "Deformation theory and quantum groups with applications to mathematical physics (Amherst, MA, 1990)", Contemp. Math. 134, Amer. Math. Soc. (1992) 235–245 MR1187291
337 J H Przytycki, Vassiliev–Gusarov skein modules of 3–manifolds and criteria for periodicity of knots, from: "Low-dimensional topology (Knoxville, TN, 1992)", Conf. Proc. Lecture Notes Geom. Topology, III, Int. Press, Cambridge, MA (1994) 143–162 MR1316179
338 J H Przytycki, 3–coloring and other elementary invariants of knots, from: "Knot theory (Warsaw, 1995)", Banach Center Publ. 42, Polish Acad. Sci. (1998) 275–295 MR1634462
339 J H Przytycki, A q–analogue of the first homology group of a 3–manifold, from: "Perspectives on quantization (South Hadley, MA, 1996)", Contemp. Math. 214, Amer. Math. Soc. (1998) 135–144 MR1601241
340 J H Przytycki, Fundamentals of Kauffman bracket skein modules, Kobe J. Math. 16 (1999) 45–66 MR1723531
341 J H Przytycki, Kauffman bracket skein module of a connected sum of 3–manifolds, Manuscripta Math. 101 (2000) 199–207 MR1742248
342 J H Przytycki, Homotopy and q–homotopy skein modules of 3–manifolds: an example in algebra situs, from: "Knots, braids, and mapping class groups—papers dedicated to Joan S. Birman (New York, 1998)", AMS/IP Stud. Adv. Math. 24, Amer. Math. Soc. (2001) 143–170 MR1873115
343 J H Przytycki, Skein module deformations of elementary moves on links, from: "Invariants of knots and 3–manifolds (Kyoto, 2001)", Geom. Topol. Monogr. 4, Geom. Topol. Publ., Coventry (2002) 313–335 MR2048107
344 J H Przytycki, A S Sikora, Skein algebra of a group, from: "Knot theory (Warsaw, 1995)", Banach Center Publ. 42, Polish Acad. Sci. (1998) 297–306 MR1634463
345 J H Przytycki, A S Sikora, On skein algebras and Sl2(C)–character varieties, Topology 39 (2000) 115–148 MR1710996
346 J H Przytycki, T Tsukamoto, The fourth skein module and the Montesinos–Nakanishi conjecture for 3–algebraic links, J. Knot Theory Ramifications 10 (2001) 959–982 MR1867103
347 N Reshetikhin, V G Turaev, Invariants of 3–manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991) 547–597 MR1091619
348 J Roberts, Classical 6j–symbols and the tetrahedron, Geom. Topol. 3 (1999) 21–66 MR1673272
349 J Roberts, Rozansky–Witten theory, from: "Topology and geometry of manifolds (Athens, GA, 2001)", Proc. Sympos. Pure Math. 71, Amer. Math. Soc. (2003) 1–17 MR2024627
350 J Roberts, J Sawon, Generalisations of Rozansky–Witten invariants, from: "Invariants of knots and 3–manifolds (Kyoto, 2001)", Geom. Topol. Monogr. 4, Geom. Topol. Publ., Coventry (2002) 263–279 MR2002615
351 J D Roberts, J Sawon, S Willerton, The Rozansky–Witten TQFT, in preparation
352 J D Roberts, S Willerton, On the Rozansky–Witten weight systems, in preparation
353 Y Rong, Link polynomials of higher order, J. London Math. Soc. (2) 56 (1997) 189–208 MR1462835
354 L Rozansky, Witten's invariant of 3–dimensional manifolds: loop expansion and surgery calculus, from: "Knots and applications", Ser. Knots Everything 6, World Sci. Publ., River Edge, NJ (1995) 271–299 MR1364193
355 L Rozansky, A large k asymptotics of Witten's invariant of Seifert manifolds, Comm. Math. Phys. 171 (1995) 279–322 MR1344728
356 L Rozansky, Residue formulas for the large k asymptotics of Witten's invariants of Seifert manifolds. The case of SU(2), Comm. Math. Phys. 178 (1996) 27–60 MR1387940
357 L Rozansky, On p–adic convergence of perturbative invariants of some rational homology spheres, Duke Math. J. 91 (1998) 353–379 MR1600594
358 L Rozansky, On p–adic properties of the Witten–Reshetikhin–Turaev invariant, from: "Primes and knots", Contemp. Math. 416, Amer. Math. Soc. (2006) 213–236 MR2276143
359 L Rozansky, A rational structure of generating functions for Vassiliev invariants, lecture notes, summer school “Quantum invariants of knots and three-manifolds”, Grenoble, June 1999
360 L Rozansky, A rationality conjecture about Kontsevich integral of knots and its implications to the structure of the colored Jones polynomial, from: "Proceedings of the Pacific Institute for the Mathematical Sciences Workshop “Invariants of Three–Manifolds” (Calgary, AB, 1999)" (2003) 47–76 MR1953320
361 L Rozansky, pol2.mws, Maple V computer program
362 L Rozansky, E Witten, Hyper–Kähler geometry and invariants of three-manifolds, Selecta Math. (N.S.) 3 (1997) 401–458 MR1481135
363 L Rozansky, E Witten, Hyper–Kähler geometry and invariants of three-manifolds, Selecta Math. (N.S.) 3 (1997) 401–458 MR1481135
364 L Rudolph, Nontrivial positive braids have positive signature, Topology 21 (1982) 325–327 MR649763
365 N Sato, Constructing a nondegenerate commuting square from equivalent systems of bimodules, Internat. Math. Res. Notices (1997) 967–981 MR1488347
366 N Saveliev, Lectures on the topology of 3–manifolds, de Gruyter Textbook, Walter de Gruyter & Co. (1999) MR1712769 An introduction to the Casson invariant
367 J Sawon, The Rozansky–Witten invariants of hyper–Kähler manifolds, from: "Differential geometry and applications (Brno, 1998)", Masaryk Univ. (1999) 429–436 MR1708931
368 Y Shinohara, On the signature of knots and links, Trans. Amer. Math. Soc. 156 (1971) 273–285 MR0275415
369 N Shirokova, The space of 3–manifolds, C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 131–136 MR1781529
370 A S Sikora, Skein modules at the 4th roots of unity, J. Knot Theory Ramifications 13 (2004) 571–585 MR2080123
371 A S Sikora, SLn–character varieties as spaces of graphs, Trans. Amer. Math. Soc. 353 (2001) 2773–2804 MR1828473
372 A S Sikora, Analogies between group actions on 3–manifolds and number fields, Comment. Math. Helv. 78 (2003) 832–844 MR2016698
373 J M Sink, A zeta-function for a knot using SL2(Fps) representations, from: "Knots in Hellas '98 (Delphi)", Ser. Knots Everything 24, World Sci. Publ., River Edge, NJ (2000) 452–470 MR1865723
374 T B Stanford, Computing Vassiliev's invariants, Topology Appl. 77 (1997) 261–276 MR1451588
375 T B Stanford, Vassiliev invariants and knots modulo pure braid subgroups arXiv:math.GT/9805092
376 T B Stanford, Braid commutators and delta finite-type invariants, from: "Knots in Hellas '98 (Delphi)", Ser. Knots Everything 24, World Sci. Publ., River Edge, NJ (2000) 471–476 MR1865724
377 A Stoimenow, Enumeration of chord diagrams and an upper bound for Vassiliev invariants, J. Knot Theory Ramifications 7 (1998) 93–114 MR1611987
378 A Stoimenow, Square numbers, spanning trees and invariants of achiral knots, Comm. Anal. Geom. 13 (2005) 591–631 MR2171693
379 A Stoimenow, On finiteness of Vassiliev invariants and a proof of the Lin–Wang conjecture via braiding polynomials, J. Knot Theory Ramifications 10 (2001) 769–780 MR1839701 Knots in Hellas '98, Vol. 3 (Delphi)
380 A Stoimenow, Knots of (canonical) genus two, Fund. Math. 200 (2008) 1–67 MR2443760
381 T Takata, On quantum PSU(n)–invariants for lens spaces, J. Knot Theory Ramifications 5 (1996) 885–901 MR1422132
382 T Takata, On quantum PSU(n) invariants for Seifert manifolds, J. Knot Theory Ramifications 6 (1997) 417–426 MR1457196
383 K Taniyama, A partial order of knots, Tokyo J. Math. 12 (1989) 205–229 MR1001742
384 V Tchernov, Vassiliev invariants of Legendrian, transverse, and framed knots in contact three-manifolds, Topology 42 (2003) 1–33 MR1928643
385 D P Thurston, Integral expressions for the Vassiliev knot invariants arXiv:math.QA/9901110
386 D P Thurston, Hyperbolic volume and the Jones polynomial, lecture notes, summer school “Quantum invariants of knots and three-manifolds”, Grenoble, June 1999
387 D P Thurston, Wheeling: A diagrammatic analogue of the Duflo isomorphism, PhD thesis, University of California at Berkeley (2000) arXiv:math.QA/0006083
388 D P Thurston, lecture notes, Research Institute for Mathematical Sciences, Kyoto University, October–November 2001
389 A G Tristram, Some cobordism invariants for links, Proc. Cambridge Philos. Soc. 66 (1969) 251–264 MR0248854
390 V G Turaev, The Conway and Kauffman modules of a solid torus, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 167 (1988) 79–89, 190 MR964255
391 V G Turaev, Skein quantization of Poisson algebras of loops on surfaces, Ann. Sci. École Norm. Sup. (4) 24 (1991) 635–704 MR1142906
392 V G Turaev, Quantum invariants of knots and 3–manifolds, de Gruyter Studies in Mathematics 18, Walter de Gruyter & Co. (1994) MR1292673
393 V G Turaev, Homotopy field theory in dimension 2 and group-algebras arXiv:math.QA/9910010
394 V G Turaev, Homotopy field theory in dimension 3 and crossed group-categories arXiv:math.GT/0005291
395 V G Turaev, Surgery formula for torsions and Seiberg–Witten invariants of 3–manifolds arXiv:math.GT/0101108
396 V G Turaev, O Y Viro, State sum invariants of 3–manifolds and quantum 6j–symbols, Topology 31 (1992) 865–902 MR1191386
397 V A Vassiliev, Cohomology of knot spaces, from: "Theory of singularities and its applications", Adv. Soviet Math. 1, Amer. Math. Soc. (1990) 23–69 MR1089670
398 E Verlinde, Fusion rules and modular transformations in 2D conformal field theory, Nuclear Phys. B 300 (1988) 360–376 MR954762
399 P Vogel, Algebraic structures on modules of diagrams, preprint (1996)
400 P Vogel, The universal Lie algebra, lecture notes, summer school “Quantum invariants of knots and three-manifolds”, Grenoble, June 1999
401 P Vogel, in preparation
402 K Walker, An extension of Casson's invariant, Annals of Mathematics Studies 126, Princeton University Press (1992) MR1154798
403 D J A Welsh, The computational complexity of knot and matroid polynomials, Discrete Math. 124 (1994) 251–269 MR1258858 Graphs and combinatorics (Qawra, 1990)
404 B W Westbury, A generating function for spin network evaluations, from: "Knot theory (Warsaw, 1995)", Banach Center Publ. 42, Polish Acad. Sci. (1998) 447–456 MR1634471
405 S Willerton, On the first two Vassiliev invariants, Experiment. Math. 11 (2002) 289–296 MR1959269
406 S Willerton, An almost-integral universal Vassiliev invariant of knots, Algebr. Geom. Topol. 2 (2002) 649–664 MR1928173
407 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351–399 MR990772
408 E Witten, Chern–Simons gauge theory as a string theory, from: "The Floer memorial volume", Progr. Math. 133, Birkhäuser (1995) 637–678 MR1362846
409 F Y Wu, J Wang, Zeroes of the Jones polynomial, Phys. A 296 (2001) 483–494 MR1840867
410 S Yamada, The absolute value of the Chern–Simons–Witten invariants of lens spaces, J. Knot Theory Ramifications 4 (1995) 319–327 MR1331752
411 S Yamada, How to find knots with unit Jones polynomials, from: "Knot Theory: Proceedings of the conference dedicated to Professor Kunio Murasugi for his 70th birthday, Toronto, July 13th-17th 1999" (2000) 355–361
412 Y Yokota, Skeins and quantum SU(N) invariants of 3–manifolds, Math. Ann. 307 (1997) 109–138 MR1427678
413 Y Yokota, On the volume conjecture for hyperbolic knots arXiv:math.QA/0009165
414 D Zagier, Vassiliev invariants and a strange identity related to the Dedekind eta-function, Topology 40 (2001) 945–960 MR1860536
415 J K Zhong, The Kauffman skein module of a connected sum of 3–manifolds, Topology Appl. 139 (2004) 113–128 MR2051100
416 J K Zhong, B Lu, On the Kauffman skein modules, Manuscripta Math. 109 (2002) 29–47 MR1931206
417 M G Zinno, On Krammer's representation of the braid group, Math. Ann. 321 (2001) 197–211 MR1857374