Volume 19, issue 7 (2019)

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

Volume 22
Issue 6, 2533–3057
Issue 5, 2007–2532
Issue 4, 1497–2006
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

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
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
On Kauffman bracket skein modules of marked $3$–manifolds and the Chebyshev–Frobenius homomorphism

Thang T Q Lê and Jonathan Paprocki

Algebraic & Geometric Topology 19 (2019) 3453–3509
Bibliography
1 F Bonahon, Miraculous cancellations for quantum SL2, preprint (2017) arXiv:1708.07617
2 F Bonahon, H Wong, Quantum traces for representations of surface groups in SL2(), Geom. Topol. 15 (2011) 1569 MR2851072
3 F Bonahon, H Wong, Representations of the Kauffman bracket skein algebra, I : Invariants and miraculous cancellations, Invent. Math. 204 (2016) 195 MR3480556
4 D Bullock, Rings of SL2()–characters and the Kauffman bracket skein module, Comment. Math. Helv. 72 (1997) 521 MR1600138
5 S Fomin, M Shapiro, D Thurston, Cluster algebras and triangulated surfaces, I : Cluster complexes, Acta Math. 201 (2008) 83 MR2448067
6 M Freedman, J Hass, P Scott, Closed geodesics on surfaces, Bull. London Math. Soc. 14 (1982) 385 MR671777
7 C Frohman, R Gelca, Skein modules and the noncommutative torus, Trans. Amer. Math. Soc. 352 (2000) 4877 MR1675190
8 C Frohman, J Kania-Bartoszynska, T Lê, Unicity for representations of the Kauffman bracket skein algebra, Invent. Math. 215 (2019) 609 MR3910071
9 K R Goodearl, R B Warfield Jr., An introduction to noncommutative Noetherian rings, 61, Cambridge Univ. Press (2004) MR2080008
10 V F R Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985) 103 MR766964
11 V Kac, P Cheung, Quantum calculus, Springer (2002) MR1865777
12 L H Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395 MR899057
13 T T Q Lê, The colored Jones polynomial and the A–polynomial of knots, Adv. Math. 207 (2006) 782 MR2271986
14 T T Q Lê, On Kauffman bracket skein modules at roots of unity, Algebr. Geom. Topol. 15 (2015) 1093 MR3342686
15 T T Q Lê, The colored Jones polynomial and the AJ conjecture, from: "Lectures on quantum topology in dimension three" (editors T T Q Lê, C Lescop, R Lipshitz, P Turner), Panor. Synthèses 48, Soc. Math. France (2016) 33 MR3617632
16 T T Q Lê, On positivity of Kauffman bracket skein algebras of surfaces, Int. Math. Res. Not. 2018 (2018) 1314 MR3801463
17 T T Q Lê, Quantum Teichmüller spaces and quantum trace map, J. Inst. Math. Jussieu 18 (2019) 249 MR3915288
18 J Marché, The Kauffman skein algebra of a surface at √ − 1, Math. Ann. 351 (2011) 347 MR2836662
19 G Muller, Skein and cluster algebras of marked surfaces, Quantum Topol. 7 (2016) 435 MR3551171
20 R C Penner, Decorated Teichmüller theory, European Mathematical Society (2012) MR3052157
21 J H Przytycki, Fundamentals of Kauffman bracket skein modules, Kobe J. Math. 16 (1999) 45 MR1723531
22 J H Przytycki, A S Sikora, On skein algebras and Sl2()–character varieties, Topology 39 (2000) 115 MR1710996
23 J H Przytycki, A S Sikora, Skein algebras of surfaces, Trans. Amer. Math. Soc. 371 (2019) 1309 MR3885180
24 A S Sikora, Skein modules at the 4th roots of unity, J. Knot Theory Ramifications 13 (2004) 571 MR2080123
25 D P Thurston, Positive basis for surface skein algebras, Proc. Natl. Acad. Sci. USA 111 (2014) 9725 MR3263305
26 V G Turaev, The Conway and Kauffman modules of a solid torus, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 167 (1988) 79 MR964255
27 V G Turaev, Skein quantization of Poisson algebras of loops on surfaces, Ann. Sci. École Norm. Sup. 24 (1991) 635 MR1142906