On Kauffman bracket skein modules at roots of unity
Algebraic and Geometric Topology, Tome 15 (2015) no. 2, pp. 1093-1117
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We reprove and expand results of Bonahon and Wong on central elements of the Kauffman bracket skein modules at roots of 1 and on the existence of the Chebyshev homomorphism, using elementary skein methods.

DOI : 10.2140/agt.2015.15.1093
Keywords: Kauffman bracket skein module, Chebyshev homomorphism

Lê, Thang  1

1 School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332, USA
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Lê, Thang. On Kauffman bracket skein modules at roots of unity. Algebraic and Geometric Topology, Tome 15 (2015) no. 2, pp. 1093-1117. doi: 10.2140/agt.2015.15.1093

[1] C Blanchet, N Habegger, G Masbaum, P Vogel, Three-manifold invariants derived from the Kauffman bracket, Topology 31 (1992) 685

[2] F Bonahon, H Wong, Representations of the Kauffman skein algebra I: Invariants and miraculous cancellations,

[3] F Bonahon, H Wong, Quantum traces for representations of surface groups in $\mathrm{SL}_2(\mathbb C)$, Geom. Topol. 15 (2011) 1569

[4] D Bullock, Rings of $\mathrm{SL}_2(\mathbb{C})$–characters and the Kauffman bracket skein module, Comment. Math. Helv. 72 (1997) 521

[5] D Bullock, C Frohman, J Kania-Bartoszyńska, Understanding the Kauffman bracket skein module, J. Knot Theory Ramifications 8 (1999) 265

[6] D Bullock, J H Przytycki, Multiplicative structure of Kauffman bracket skein module quantizations, Proc. Amer. Math. Soc. 128 (2000) 923

[7] V V Fok, L O Chekhov, Quantum Teichmüller spaces, Teoret. Mat. Fiz. 120 (1999) 511

[8] C Frohman, R Gelca, Skein modules and the noncommutative torus, Trans. Amer. Math. Soc. 352 (2000) 4877

[9] R M Kashaev, Quantization of Teichmüller spaces and the quantum dilogarithm, Lett. Math. Phys. 43 (1998) 105

[10] L H Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395

[11] T T Q Lê, The colored Jones polynomial and the $A$–polynomial of knots, Adv. Math. 207 (2006) 782

[12] T T Q Lê, A T Tran, The Kauffman bracket skein module of two-bridge links, Proc. Amer. Math. Soc. 142 (2014) 1045

[13] W B R Lickorish, An introduction to knot theory, Graduate Texts in Math. 175, Springer (1997)

[14] J Marché, The skein module of torus knots, Quantum Topol. 1 (2010) 413

[15] J H Przytycki, Fundamentals of Kauffman bracket skein modules, Kobe J. Math. 16 (1999) 45

[16] J H Przytycki, A S Sikora, On skein algebras and $\mathrm{SL}_2(\mathbb{C})$–character varieties, Topology 39 (2000) 115

[17] A S Sikora, Skein modules at the $4^{\text{th}}$ roots of unity, J. Knot Theory Ramifications 13 (2004) 571

[18] V G Turaev, Skein quantization of Poisson algebras of loops on surfaces, Ann. Sci. École Norm. Sup. 24 (1991) 635

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