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Representations of the Kauffman bracket skein algebra, II: Punctured surfaces

Francis Bonahon and Helen Wong

Algebraic & Geometric Topology 17 (2017) 3399–3434
Bibliography
1 N Abdiel, C Frohman, The localized skein algebra is Frobenius, preprint (2015) arXiv:1501.02631
2 J W Barrett, Skein spaces and spin structures, Math. Proc. Cambridge Philos. Soc. 126 (1999) 267 MR1670233
3 C Blanchet, N Habegger, G Masbaum, P Vogel, Topological quantum field theories derived from the Kauffman bracket, Topology 34 (1995) 883 MR1362791
4 F Bonahon, Shearing hyperbolic surfaces, bending pleated surfaces and Thurston’s symplectic form, Ann. Fac. Sci. Toulouse Math. 5 (1996) 233 MR1413855
5 F Bonahon, X Liu, Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms, Geom. Topol. 11 (2007) 889 MR2326938
6 F Bonahon, H Wong, Kauffman brackets, character varieties and triangulations of surfaces, from: "Topology and geometry in dimension three" (editors W Li, L Bartolini, J Johnson, F Luo, R Myers, J H Rubinstein), Contemp. Math. 560, Amer. Math. Soc. (2011) 179 MR2866931
7 F Bonahon, H Wong, Quantum traces for representations of surface groups in SL2(), Geom. Topol. 15 (2011) 1569 MR2851072
8 F Bonahon, H Wong, The Witten–Reshetikhin–Turaev representation of the Kauffman bracket skein algebra, Proc. Amer. Math. Soc. 144 (2016) 2711 MR3477089
9 F Bonahon, H Wong, Representations of the Kauffman bracket skein algebra, I : Invariants and miraculous cancellations, Invent. Math. 204 (2016) 195 MR3480556
10 F Bonahon, H Wong, Representations of the Kauffman bracket skein algebra, III: Closed surfaces and naturality, preprint (2015) arXiv:1505.01522
11 F Bonahon, H Wong, Representations of the Kauffman bracket skein algebra, IV: Naturality for punctured surfaces, in preparation
12 D Bullock, Estimating a skein module with SL2(C) characters, Proc. Amer. Math. Soc. 125 (1997) 1835 MR1403115
13 D Bullock, Rings of SL2(C)–characters and the Kauffman bracket skein module, Comment. Math. Helv. 72 (1997) 521 MR1600138
14 D Bullock, C Frohman, J Kania-Bartoszyńska, Understanding the Kauffman bracket skein module, J. Knot Theory Ramifications 8 (1999) 265 MR1691437
15 D Bullock, C Frohman, J Kania-Bartoszyńska, The Kauffman bracket skein as an algebra of observables, Proc. Amer. Math. Soc. 130 (2002) 2479 MR1897475
16 D Bullock, J H Przytycki, Multiplicative structure of Kauffman bracket skein module quantizations, Proc. Amer. Math. Soc. 128 (2000) 923 MR1625701
17 L O Chekhov, V V Fock, Observables in 3D gravity and geodesic algebras, Czechoslovak J. Phys. 50 (2000) 1201 MR1806262
18 V V Fock, Dual Teichmüller spaces, unpublished preprint (1997) arXiv:dg-ga/9702018
19 V V Fok, L O Chekhov, Quantum Teichmüller spaces, Teoret. Mat. Fiz. 120 (1999) 511 MR1737362
20 C Frohman, N Abdiel, Frobenius algebras derived from the Kauffman bracket skein algebra, J. Knot Theory Ramifications 25 (2016) 1 MR3482494
21 C Frohman, J Kania-Bartoszyńska, The structure of the Kauffman bracket skein algebra at roots of unity, preprint (2016) arXiv:1607.03424
22 C Frohman, J Kania-Bartoszyńska, T T Q Lê, Unicity for representations of the Kauffman bracket skein algebra, preprint (2017) arXiv:1707.09234
23 M Havlíček, S Pošta, On the classification of irreducible finite-dimensional representations of Uq(so3) algebra, J. Math. Phys. 42 (2001) 472 MR1808791
24 R M Kashaev, Quantization of Teichmüller spaces and the quantum dilogarithm, Lett. Math. Phys. 43 (1998) 105 MR1607296
25 T T Q Lê, On Kauffman bracket skein modules at roots of unity, Algebr. Geom. Topol. 15 (2015) 1093 MR3342686
26 X Liu, The quantum Teichmüller space as a noncommutative algebraic object, J. Knot Theory Ramifications 18 (2009) 705 MR2527682
27 D Mumford, J Fogarty, F Kirwan, Geometric invariant theory, 34, Springer (1994) MR1304906
28 R C Penner, J L Harer, Combinatorics of train tracks, 125, Princeton Univ. Press (1992) MR1144770
29 J H Przytycki, A S Sikora, On skein algebras and Sl2(C)–character varieties, Topology 39 (2000) 115 MR1710996
30 N Reshetikhin, V G Turaev, Invariants of 3–manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991) 547 MR1091619
31 N Takenov, Representations of the Kauffman skein algebra of small surfaces, preprint (2015) arXiv:1504.04573
32 W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
33 V G Turaev, Skein quantization of Poisson algebras of loops on surfaces, Ann. Sci. École Norm. Sup. 24 (1991) 635 MR1142906
34 V G Turaev, Quantum invariants of knots and 3–manifolds, 18, de Gruyter (1994) MR1292673
35 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351 MR990772