Volume 16, issue 2 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 7, 3217–3753
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

Author Index
The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
To Appear
 
Other MSP Journals
Finite-type invariants of w-knotted objects, I: w-knots and the Alexander polynomial

Dror Bar-Natan and Zsuzsanna Dancso

Algebraic & Geometric Topology 16 (2016) 1063–1133
Bibliography
1 A Alekseev, B Enriquez, C Torossian, Drinfeld associators, braid groups and explicit solutions of the Kashiwara–Vergne equations, Publ. Math. Inst. Hautes Études Sci. (2010) 143 MR2737979
2 A Alekseev, C Torossian, The Kashiwara–Vergne conjecture and Drinfeld’s associators, Ann. of Math. 175 (2012) 415 MR2877064
3 Z Amir-Khosravi, S Sankaran, VasCalc: a Vassiliev invariants calculator,
4 E Artin, Theory of braids, Ann. of Math. 48 (1947) 101 MR0019087
5 J C Baez, D K Wise, A S Crans, Exotic statistics for strings in 4D BF theory, Adv. Theor. Math. Phys. 11 (2007) 707 MR2362007
6 D Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995) 423 MR1318886
7 D Bar-Natan, Vassiliev homotopy string link invariants, J. Knot Theory Ramifications 4 (1995) 13 MR1321289
8 D Bar-Natan, Some computations related to Vassiliev invariants, (1996)
9 D Bar-Natan, Vassiliev and quantum invariants of braids, from: "The interface of knots and physics" (editor L H Kauffman), Proc. Sympos. Appl. Math. 51, Amer. Math. Soc. (1996) 129 MR1372767
10 D Bar-Natan, Non-associative tangles, from: "Geometric topology" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 139 MR1470726
11 D Bar-Natan, On associators and the Grothendieck–Teichmuller group, I, Selecta Math. 4 (1998) 183 MR1669949
12 D Bar-Natan, Algebraic knot theory —a call for action, web document (2006)
13 D Bar-Natan, Finite-type invariants, from: "Encyclopedia of Mathematical Physics" (editors J P Françoise, G L Naber, T S Tsun), Elsevier (2006)
14 D Bar-Natan, Balloons and hoops and their universal finite-type invariant, BF theory, and an ultimate Alexander invariant, Acta Math. Vietnam. 40 (2015) 271 MR3366171
15 D Bar-Natan, Z Dancso, Finite type invariants of w-knotted objects: from Alexander to Kashiwara and Vergne, web version of the first and second papers in one, videos (wClips) and related files
16 D Bar-Natan, Z Dancso, Finite type invariants of w-knotted objects, II: Tangles and the Kashiwara-Vergne problem, preprint (2014) arXiv:1405.1955
17 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. 8 (2002) 315 MR1931167
18 D Bar-Natan, S Garoufalidis, L Rozansky, D P Thurston, The Århus integral of rational homology 3–spheres, II : Invariance and universality, Selecta Math. 8 (2002) 341 MR1931168
19 D Bar-Natan, S Garoufalidis, L Rozansky, D P Thurston, The Århus integral of rational homology 3–spheres, III : Relation with the Le–Murakami–Ohtsuki invariant, Selecta Math. 10 (2004) 305 MR2099069
20 D Bar-Natan, I Halacheva, L Leung, F Roukema, Some dimensions of spaces of finite type invariants of virtual knots, Exp. Math. 20 (2011) 282 MR2836253
21 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 MR1988280
22 D Bar-Natan, S Selmani, Meta-monoids, meta-bicrossed products, and the Alexander polynomial, J. Knot Theory Ramifications 22 (2013) MR3125897
23 D Bar-Natan, A Stoimenow, The fundamental theorem of Vassiliev invariants, from: "Geometry and physics" (editors J E Andersen, J Dupont, H Pedersen, A Swann), Lecture Notes in Pure and Appl. Math. 184, Dekker (1997) 101 MR1423158
24 V G Bardakov, The virtual and universal braids, Fund. Math. 184 (2004) 1 MR2128039
25 V G Bardakov, P Bellingeri, Combinatorial properties of virtual braids, Topology Appl. 156 (2009) 1071 MR2493369
26 B Berceanu, Ş Papadima, Universal representations of braid and braid-permutation groups, J. Knot Theory Ramifications 18 (2009) 999 MR2549480
27 R Bott, C Taubes, On the self-linking of knots, J. Math. Phys. 35 (1994) 5247 MR1295465
28 T E Brendle, A Hatcher, Configuration spaces of rings and wickets, Comment. Math. Helv. 88 (2013) 131 MR3008915
29 J S Carter, M Saito, Knotted surfaces and their diagrams, 55, Amer. Math. Soc. (1998) MR1487374
30 A S Cattaneo, P Cotta-Ramusino, J Fröhlich, M Martellini, Topological BF theories in 3 and 4 dimensions, J. Math. Phys. 36 (1995) 6137 MR1355902
31 A S Cattaneo, P Cotta-Ramusino, M Martellini, Three-dimensional BF theories and the Alexander–Conway invariant of knots, Nuclear Phys. B 436 (1995) 355 MR1316372
32 Z Dancso, On the Kontsevich integral for knotted trivalent graphs, Algebr. Geom. Topol. 10 (2010) 1317 MR2661529
33 V G Drinfel’d, Quantum groups, from: "Proceedings of the International Congress of Mathematicians, I, II" (editor A M Gleason), Amer. Math. Soc. (1987) 798 MR934283
34 V G Drinfel’d, Quasi-Hopf algebras, Algebra i Analiz 1 (1989) 114 MR1047964
35 V G Drinfel’d, On quasitriangular quasi-Hopf algebras and on a group that is closely connected with Gal(Q∕Q), Algebra i Analiz 2 (1990) 149 MR1080203
36 H A Dye, Virtual knots undetected by 1– and 2–strand bracket polynomials, Topology Appl. 153 (2005) 141 MR2172041
37 D B A Epstein, Word processing in groups, A K Peters (1992)
38 P Etingof, D Kazhdan, Quantization of Lie bialgebras, I, Selecta Math. 2 (1996) 1 MR1403351
39 R Fenn, R Rimányi, C Rourke, The braid-permutation group, Topology 36 (1997) 123 MR1410467
40 D L Goldsmith, The theory of motion groups, Michigan Math. J. 28 (1981) 3 MR600411
41 M Goussarov, Finite type invariants and n–equivalence of 3–manifolds, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 517 MR1715131
42 M Goussarov, M Polyak, O Viro, Finite-type invariants of classical and virtual knots, Topology 39 (2000) 1045 MR1763963
43 M Gusarov, On n–equivalence of knots and invariants of finite degree, from: "Topology of manifolds and varieties" (editor O Viro), Adv. Soviet Math. 18, Amer. Math. Soc. (1994) 173 MR1296895
44 M Gutiérrez, S Krstić, Normal forms for basis-conjugating automorphisms of a free group, Internat. J. Algebra Comput. 8 (1998) 631 MR1682236
45 N Habegger, G Masbaum, The Kontsevich integral and Milnor’s invariants, Topology 39 (2000) 1253 MR1783857
46 K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1 MR1735632
47 K Habiro, T Kanenobu, A Shima, Finite type invariants of ribbon 2–knots, from: "Low-dimensional topology" (editor H Nencka), Contemp. Math. 233, Amer. Math. Soc. (1999) 187 MR1701683
48 K Habiro, A Shima, Finite type invariants of ribbon 2–knots, II, Topology Appl. 111 (2001) 265 MR1814229
49 A Haviv, Towards a diagrammatic analogue of the Reshetikhin–Turaev link invariants, PhD thesis, Hebrew University (2002) arXiv:math.QA/0211031
50 D Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982) 37 MR638121
51 T Kanenobu, A Shima, Two filtrations of ribbon 2–knots, Topology Appl. 121 (2002) 143 MR1903688
52 M Kashiwara, M Vergne, The Campbell–Hausdorff formula and invariant hyperfunctions, Invent. Math. 47 (1978) 249 MR0492078
53 L H Kauffman, On knots, 115, Princeton Univ. Press (1987) MR907872
54 L H Kauffman, Virtual knot theory, European J. Combin. 20 (1999) 663 MR1721925
55 L H Kauffman, S Lambropoulou, Virtual braids, Fund. Math. 184 (2004) 159 MR2128049
56 J A Kneissler, The number of primitive Vassiliev invariants up to degree twelve, preprint (1997) arXiv:q-alg/9706022
57 T Kohno, Vassiliev invariants and de Rham complex on the space of knots, from: "Symplectic geometry and quantization" (editors Y Maeda, H Omori, A Weinstein), Contemp. Math. 179, Amer. Math. Soc. (1994) 123 MR1319605
58 A Kricker, The lines of the Kontsevich integral and Rozansky’s rationality conjecture, preprint (2000) arXiv:math/0005284
59 G Kuperberg, What is a virtual link?, Algebr. Geom. Topol. 3 (2003) 587 MR1997331
60 V Kurlin, Compressed Drinfeld associators, Journal of Algebra 292 (2005) 184 MR2166802
61 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" (editors V M Buchstaber, S P Novikov), Amer. Math. Soc. Transl. Ser. 2 179 (1997) 75
62 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 MR1320252
63 T Q T Le, J Murakami, The universal Vassiliev–Kontsevich invariant for framed oriented links, Compositio Math. 102 (1996) 41 MR1394520
64 T T Q Le, J Murakami, T Ohtsuki, On a universal perturbative invariant of 3–manifolds, Topology 37 (1998) 539 MR1604883
65 P Lee, Closed-form associators and braidors in a partly commutative quotient, preprint (2007)
66 P Lee, The pure virtual braid group is quadratic, Selecta Math. 19 (2013) 461 MR3090235
67 P Lee, Proof of a conjectured formula for the Alexander invariant, J. Knot Theory Ramifications 23 (2014) MR3298210
68 C Lescop, On the cube of the equivariant linking pairing for 3–manifolds of rank one, preprint arXiv:1008.5026
69 C Lescop, Invariants of knots and 3–manifolds derived from the equivariant linking pairing, from: "Chern–Simons gauge theory : 20 years after" (editors J E Andersen, H U Boden, A Hahn, B Himpel), AMS/IP Stud. Adv. Math. 50, Amer. Math. Soc. (2011) 217 MR2809454
70 L Leung, Combinatorial formulas for classical Lie weight systems on arrow diagrams, preprint (2008) arXiv:0812.2342
71 J Lieberum, The Drinfeld associator of gl(1|1), from: "Quantum groups" (editor B Enriquez), IRMA Lect. Math. Theor. Phys. 12, Eur. Math. Soc. (2008) 39 MR2432989
72 X S Lin, Power series expansions and invariants of links, from: "Geometric topology" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 184 MR1470727
73 W Magnus, A Karrass, D Solitar, Combinatorial group theory : Presentations of groups in terms of generators and relations, Interscience (1966) MR0207802
74 J McCool, On basis-conjugating automorphisms of free groups, Canad. J. Math. 38 (1986) 1525 MR873421
75 J W Milnor, J C Moore, On the structure of Hopf algebras, Ann. of Math. 81 (1965) 211 MR0174052
76 G Naot, On Chern–Simons theory with an inhomogeneous gauge group and BF theory knot invariants, J. Math. Phys. 46 (2005) MR2194021
77 T Ohtsuki, Finite type invariants of integral homology 3–spheres, J. Knot Theory Ramifications 5 (1996) 101 MR1373813
78 M Polyak, On the algebra of arrow diagrams, Lett. Math. Phys. 51 (2000) 275 MR1778064
79 D Rolfsen, Knots and links, 7, Publish or Perish (1990) MR1277811
80 F Roukema, Goussarov–Polyak–Viro combinatorial formulas for finite type invariants, preprint (2007) arXiv:0711.4001
81 S Satoh, Virtual knot presentation of ribbon torus-knots, J. Knot Theory Ramifications 9 (2000) 531 MR1758871
82 D Thurston, Integral expressions for the Vassiliev knot invariants, senior thesis, Harvard University (1995) arXiv:math.QA/9901110
83 V A Vassiliev, Cohomology of knot spaces, from: "Theory of singularities and its applications" (editor V I Arnol’d), Adv. Soviet Math. 1, Amer. Math. Soc. (1990) 23 MR1089670
84 T Watanabe, Clasper-moves among ribbon 2–knots characterizing their finite type invariants, J. Knot Theory Ramifications 15 (2006) 1163 MR2287439