Volume 7, issue 1 (2007)

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

Volume 19
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

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Other MSP Journals
Confluence theory for graphs

Adam S Sikora and Bruce W Westbury

Algebraic & Geometric Topology 7 (2007) 439–478
Bibliography
1 J E Andersen, V Turaev, Higher skein modules, J. Knot Theory Ramifications 8 (1999) 963 MR1723433
2 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 MR1819178
3 F Baader, T Nipkow, Term rewriting and all that, Cambridge University Press (1998) MR1629216
4 G M Bergman, The diamond lemma for ring theory, Adv. in Math. 29 (1978) 178 MR506890
5 C Blanchet, N Habegger, G Masbaum, P Vogel, Topological quantum field theories derived from the Kauffman bracket, Topology 34 (1995) 883 MR1362791
6 B Bollobás, O Riordan, A polynomial of graphs on surfaces, Math. Ann. 323 (2002) 81 MR1906909
7 D Bullock, The $(2,\infty)$–skein module of the complement of a $(2,2p+1)$ torus knot, J. Knot Theory Ramifications 4 (1995) 619 MR1361084
8 D Bullock, Rings of $\mathrm{SL}_2(\mathbb{C})$–characters and the Kauffman bracket skein module, Comment. Math. Helv. 72 (1997) 521 MR1600138
9 D Bullock, C Frohman, J Kania-Bartoszyńska, Understanding the Kauffman bracket skein module, J. Knot Theory Ramifications 8 (1999) 265 MR1691437
10 D Bullock, C Frohman, J Kania-Bartoszynska, The Yang-Mills measure in the Kauffman bracket skein module, Comment. Math. Helv. 78 (2003) 1 MR1966749
11 D Bullock, J H Przytycki, Multiplicative structure of Kauffman bracket skein module quantizations, Proc. Amer. Math. Soc. 128 (2000) 923 MR1625701
12 P L Curien, Categorical combinators, sequential algorithms, and functional programming, Progress in Theoretical Computer Science, Birkhäuser (1993) MR1231971
13 H Ehrig, Introduction to the algebraic theory of graph grammars (a survey), from: "Graph-grammars and their application to computer science and biology (Internat. Workshop, Bad Honnef, 1978)", Lecture Notes in Comput. Sci. 73, Springer (1979) 1 MR565034
14 H Ehrig, Tutorial introduction to the algebraic approach of graph grammars, from: "Graph-grammars and their application to computer science (Warrenton, VA, 1986)", Lecture Notes in Comput. Sci. 291, Springer (1987) 3 MR943167
15 C Frohman, R Gelca, Skein modules and the noncommutative torus, Trans. Amer. Math. Soc. 352 (2000) 4877 MR1675190
16 C Frohman, R Gelca, W Lofaro, The $A$–polynomial from the noncommutative viewpoint, Trans. Amer. Math. Soc. 354 (2002) 735 MR1862565
17 C Frohman, J Kania-Bartoszyńska, A quantum obstruction to embedding, Math. Proc. Cambridge Philos. Soc. 131 (2001) 279 MR1857120
18 C Frohman, J Zhong, The Yang–Mills measure in the $SU_3$ skein module, preprint (2004)
19 R Gelca, J Sain, The noncommutative $A$–ideal of a $(2,2p+1)$–torus knot determines its Jones polynomial, J. Knot Theory Ramifications 12 (2003) 187 MR1967240
20 R Gelca, J Sain, The computation of the non-commutative generalization of the $A$–polynomial of the figure-eight knot, J. Knot Theory Ramifications 13 (2004) 785 MR2088746
21 P M Gilmer, J M Harris, On the Kauffman bracket skein module of the quaternionic manifold, arXiv:math.GT/0406152
22 P M Gilmer, J K Zhong, The Homflypt skein module of a connected sum of 3-manifolds, Algebr. Geom. Topol. 1 (2001) 605 MR1875610
23 R J Hadji, H R Morton, A basis for the full Homfly skein of the annulus, Math. Proc. Cambridge Philos. Soc. 141 (2006) 81 MR2238644
24 J Hoste, J H Przytycki, Homotopy skein modules of orientable 3–manifolds, Math. Proc. Cambridge Philos. Soc. 108 (1990) 475 MR1068450
25 J Hoste, J H Przytycki, A survey of skein modules of 3–manifolds, from: "Knots 90 (Osaka, 1990)", de Gruyter (1992) 363 MR1177433
26 J Hoste, J H Przytycki, The $(2,\infty)$–skein module of Whitehead manifolds, J. Knot Theory Ramifications 4 (1995) 411 MR1347362
27 J Hoste, J H Przytycki, The Kauffman bracket skein module of $S^1\times S^2$, Math. Z. 220 (1995) 65 MR1347158
28 F Jaeger, Confluent reductions of cubic plane maps (1990)
29 V F R Jones, The Potts model and the symmetric group, from: "Subfactors (Kyuzeso, 1993)", World Sci. Publ., River Edge, NJ (1994) 259 MR1317365
30 U Kaiser, Deformation of string topology into homotopy skein modules, Algebr. Geom. Topol. 3 (2003) 1005 MR2012962
31 U Kaiser, Link bordism skein modules, Fund. Math. 184 (2004) 113 MR2128047
32 U Kaiser, Quantum deformations of fundamental groups of oriented 3–manifolds, Trans. Amer. Math. Soc. 356 (2004) 3869 MR2058509
33 E Kalfagianni, X S Lin, The HOMFLY polynomial for links in rational homology 3–spheres, Topology 38 (1999) 95 MR1644083
34 L H Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395 MR899057
35 G Kuperberg, The quantum $G_2$ link invariant, Internat. J. Math. 5 (1994) 61 MR1265145
36 G Kuperberg, Spiders for rank $2$ Lie algebras, Comm. Math. Phys. 180 (1996) 109 MR1403861
37 R Lalement, Computation as logic, Prentice Hall International Series in Computer Science, Prentice Hall International (1993) MR1232661
38 T T Q Lê, The colored Jones polynomial and the $A$–polynomial of knots, Adv. Math. 207 (2006) 782 MR2271986
39 J Lieberum, Skein modules of links in cylinders over surfaces, Int. J. Math. Math. Sci. 32 (2002) 515 MR1951085
40 P Martin, Potts models and related problems in statistical mechanics, Series on Advances in Statistical Mechanics 5, World Scientific Publishing Co. (1991) MR1103994
41 J C Mitchel, Foundations for Programming Languages, MIT Press (1996)
42 M Nagl, A tutorial and bibliographical survey on graph grammars, from: "Graph-grammars and their application to computer science and biology (Internat. Workshop, Bad Honnef, 1978)", Lecture Notes in Comput. Sci. 73, Springer (1979) 70 MR565035
43 M H A Newman, On theories with a combinatorial definition of “equivalence.”, Ann. of Math. $(2)$ 43 (1942) 223 MR0007372
44 M J O’Donnell, Computing in systems described by equations, Springer (1977) MR0483644
45 E Ohlebusch, Advanced topics in term rewriting, Springer (2002) MR1934138
46 T Ohtsuki, S Yamada, Quantum $\mathrm{SU}(3)$ invariant of 3–manifolds via linear skein theory, J. Knot Theory Ramifications 6 (1997) 373 MR1457194
47 J H Przytycki, Skein modules of 3–manifolds, Bull. Polish Acad. Sci. Math. 39 (1991) 91 MR1194712
48 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 MR1184418
49 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 MR1316179
50 J H Przytycki, Algebraic topology based on knots: an introduction, from: "KNOTS '96 (Tokyo)", World Sci. Publ., River Edge, NJ (1997) 279 MR1664968
51 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 MR1601241
52 J H Przytycki, Fundamentals of Kauffman bracket skein modules, Kobe J. Math. 16 (1999) 45 MR1723531
53 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 MR1873115
54 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 MR2048107
55 J H Przytycki, From 3–moves to Lagrangian tangles and cubic skein modules, from: "Advances in topological quantum field theory", NATO Sci. Ser. II Math. Phys. Chem. 179, Kluwer Acad. Publ. (2004) 71 MR2147417
56 J H Przytycki, A S Sikora, On skein algebras and $\mathrm{Sl}_2(\mathbb{C})$–character varieties, Topology 39 (2000) 115 MR1710996
57 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 MR1867103
58 P Sallenave, Structure of the Kauffman bracket skein algebra of $T^2\times I$, J. Knot Theory Ramifications 8 (1999) 367 MR1691417
59 P Sallenave, On the Kauffman bracket skein algebra of parallelized surfaces, Ann. Sci. École Norm. Sup. $(4)$ 33 (2000) 593 MR1834496
60 A S Sikora, Skein modules and TQFT, from: "Knots in Hellas '98 (Delphi)", Ser. Knots Everything 24, World Sci. Publ., River Edge, NJ (2000) 436 MR1865721
61 A S Sikora, Skein modules at the 4th roots of unity, J. Knot Theory Ramifications 13 (2004) 571 MR2080123
62 A S Sikora, Skein theory for $\mathrm{SU}(n)$–quantum invariants, Algebr. Geom. Topol. 5 (2005) 865 MR2171796
63 C C Sims, Computation with finitely presented groups, Encyclopedia of Mathematics and its Applications 48, Cambridge University Press (1994) MR1267733
64 V G Turaev, The Conway and Kauffman modules of a solid torus, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 167 (1988) 79, 190 MR964255
65 B W Westbury, Invariant tensors for the spin representation of $\mathfrak{so}(7)$, Math. Proc. Camb. Phil. Soc. (to appear)
66 D N Yetter, On graph invariants given by linear recurrence relations, J. Combin. Theory Ser. B 48 (1990) 6 MR1047550
67 J K Zhong, The Kauffman skein module of the connected sum of 3–manifolds, arXiv:math.GT/0205131
68 J K Zhong, B Lu, On the Kauffman skein modules, Manuscripta Math. 109 (2002) 29 MR1931206