Geometry & Topology Volume 29, issue 1 (2025)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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An embedding of skein algebras of surfaces into localized quantum tori from Dehn–Thurston coordinates

Renaud Detcherry and Ramanujan Santharoubane

Geometry & Topology 29 (2025) 313–348

DOI: 10.2140/gt.2025.29.313

Bibliography

1	C Blanchet, N Habegger, G Masbaum, P Vogel, Topological quantum field theories derived from the Kauffman bracket, Topology 34 (1995) 883 MR1362791
2	F Bonahon, X Liu, Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms, Geom. Topol. 11 (2007) 889 MR2326938
3	F Bonahon, H Wong, Quantum traces for representations of surface groups in SL₂(ℂ), Geom. Topol. 15 (2011) 1569 MR2851072
4	F Bonahon, H Wong, Representations of the Kauffman bracket skein algebra, I : Invariants and miraculous cancellations, Invent. Math. 204 (2016) 195 MR3480556
5	F Bonahon, H Wong, Representations of the Kauffman bracket skein algebra, II : Punctured surfaces, Algebr. Geom. Topol. 17 (2017) 3399 MR3709650
6	F Bonahon, H Wong, Representations of the Kauffman bracket skein algebra, III : Closed surfaces and naturality, Quantum Topol. 10 (2019) 325 MR3950651
7	F Bonahon, H Wong, T Yang, Asymptotics of quantum invariants of surface diffeomorphisms, I: Conjecture and algebraic computations, preprint (2021) arXiv:2112.12852
8	D Bullock, Rings of SL₂(ℂ)-characters and the Kauffman bracket skein module, Comment. Math. Helv. 72 (1997) 521 MR1600138
9	L Charles, J Marché, Multicurves and regular functions on the representation variety of a surface in SU(2), Comment. Math. Helv. 87 (2012) 409 MR2914854
10	R Detcherry, Asymptotic formulae for curve operators in TQFT, Geom. Topol. 20 (2016) 3057 MR3590350
11	R Detcherry, T Le Fils, R Santharoubane, Compatible pants decompositions for SL₂(ℂ)-representations of surface groups, Groups Geom. Dyn. (2024)
12	C Frohman, R Gelca, Skein modules and the noncommutative torus, Trans. Amer. Math. Soc. 352 (2000) 4877 MR1675190
13	C Frohman, J Kania-Bartoszynska, T Lê, Unicity for representations of the Kauffman bracket skein algebra, Invent. Math. 215 (2019) 609 MR3910071
14	C Frohman, J Kania-Bartoszynska, T Lê, Dimension and trace of the Kauffman bracket skein algebra, Trans. Amer. Math. Soc. Ser. B 8 (2021) 510 MR4282692
15	I Ganev, D Jordan, P Safronov, The quantum Frobenius for character varieties and multiplicative quiver varieties, J. Eur. Math. Soc. (2024)
16	P M Gilmer, G Masbaum, Integral lattices in TQFT, Ann. Sci. École Norm. Sup. 40 (2007) 815 MR2382862
17	T T Q Lê, Quantum Teichmüller spaces and quantum trace map, J. Inst. Math. Jussieu 18 (2019) 249 MR3915288
18	T T Q Lê, Faithfullness of geometric action of skein algebras, Acta Math. Vietnam. 47 (2022) 279 MR4406574
19	T T Q Lê, X Zhang, Character varieties, A-polynomials and the AJ conjecture, Algebr. Geom. Topol. 17 (2017) 157 MR3604376
20	J Marché, R Santharoubane, Asymptotics of quantum representations of surface groups, Ann. Sci. École Norm. Sup. 54 (2021) 1275 MR4363245
21	G Masbaum, P Vogel, 3-Valent graphs and the Kauffman bracket, Pacific J. Math. 164 (1994) 361 MR1272656
22	J H Przytycki, Skein modules of 3-manifolds, Bull. Polish Acad. Sci. Math. 39 (1991) 91 MR1194712
23	J H Przytycki, A S Sikora, On skein algebras and Sl₂(ℂ)-character varieties, Topology 39 (2000) 115 MR1710996
24	R Santharoubane, Algebraic generators of the skein algebra of a surface, Algebr. Geom. Topol. 24 (2024) 2571 MRMR4790745
25	N Takenov, Representations of the Kauffman skein algebra of small surfaces, preprint (2015) arXiv:1504.04573
26	V G Turaev, The Conway and Kauffman modules of a solid torus, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 167 (1988) 79 MR0964255
27	V G Turaev, Skein quantization of Poisson algebras of loops on surfaces, Ann. Sci. École Norm. Sup. 24 (1991) 635 MR1142906