#### Volume 21, issue 6 (2021)

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

### Renaud Detcherry and Maxime Wolff

Algebraic & Geometric Topology 21 (2021) 2959–2993
##### Abstract

The Kauffman bracket skein module $\mathsc{𝒮}\left(M\right)$ of a $3$–manifold $M$ is a $ℚ\left(A\right)$–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 $\mathsc{𝒮}\left(\Sigma ×{S}^{1}\right)$. Combined with earlier work of Gilmer and Masbaum (Proc. Amer. Math. Soc. 147 (2019) 4091–4106), we answer their question about the dimension of $\mathsc{𝒮}\left(\Sigma ×{S}^{1}\right)$ being ${2}^{2g+1}+2g-1$.

##### Keywords
knot theory, skein modules, quantum topology
Primary: 57M27