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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 𝒮(M) of a 3–manifold M is a (A)–vector space spanned by links in M modulo the so-called Kauffman relations. For any closed oriented surface Σ we provide an explicit spanning family for the skein modules 𝒮(Σ × S1). 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(Σ × S1) being 22g+1 + 2g 1.

Keywords
knot theory, skein modules, quantum topology
Mathematical Subject Classification 2010
Primary: 57M27
References
Publication
Received: 27 January 2020
Revised: 10 July 2020
Accepted: 5 August 2020
Published: 22 November 2021
Authors
Renaud Detcherry
Max Planck Institute for Mathematics
Bonn
Germany
Institut de Mathématiques de Bourgogne
Université de Bourgogne
Dijon
France
http://detcherry.perso.math.cnrs.fr/
Maxime Wolff
Université Pierre et Marie Curie - Paris 6
Institut de Mathématiques de Jussieu
Paris
France
https://webusers.imj-prg.fr/~maxime.wolff/