Volume 19, issue 7 (2019)

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

Volume 22
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