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

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Detcherry,  Renaud
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Detcherry, R., & Wolff, M. (2021). A basis for the Kauffman skein module of the product of a surface and a circle. Algebraic & Geometric Topology, 21(6), 2959-2993. doi:10.2140/agt.2021.21.2959.


Cite as: https://hdl.handle.net/21.11116/0000-0009-B94A-4
Abstract
The Kauffman bracket skein module $S(M)$ of a 3-manifold $M$ is a
$\mathbb{Q}(A)$-vector space spanned by links in $M$ modulo the so-called
Kauffman relations. In this article, for any closed oriented surface $\Sigma$
we provide an explicit spanning family for the skein modules $S(\Sigma\times
S^1)$. Combined with earlier work of Gilmer and Masbaum, we answer their
question about the dimension of $S(\Sigma\times S^1)$ being $2^{2g+1} + 2g -1$.