A basis for the Kauffman skein module of the product of a surface and a circle

Renaud Detcherry (1, 2) , Maxime Wolff (3)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 MPIM - Max Planck Institute for Mathematics
3 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

The Kauffman bracket skein module S(M) of a 3-manifold M is a Q(A)-vector space spanned by links in M modulo the so-called Kauffman relations. For any closed oriented surface Sigma we provide an explicit spanning family for the skein modules S(Sigma x S-1). Combined with earlier work of Gilmer and Masbaum (Proc. Amer. Math. Soc. 147 (2019) 4091-4106), we answer their question about the dimension of S(Sigma x S-1) being 2(2g+1) + 2g-1.

Mots clés: Generators; knot theory; skein modules; quantum topology

Domaines: Mathématiques [math]

Renaud Detcherry, Maxime Wolff. A basis for the Kauffman skein module of the product of a surface and a circle. Algebraic and Geometric Topology, 2021, 21 (6), pp.2959-2993. ⟨10.2140/agt.2021.21.2959⟩. ⟨hal-03485334⟩