On the skein module of the product of a surface and a circle

TL;DR

This paper investigates the structure of the Kauffman bracket skein module for the product of a closed surface and a circle, establishing a lower bound on its dimension over a field of rational functions.

Contribution

It provides a new lower bound on the dimension of the skein module for Sigma x S^1, advancing understanding of its algebraic complexity.

Findings

Dimension of skein module is at least 2^{2g+1}+2g-1

Results apply to closed oriented surfaces of genus g

Enhances knowledge of skein module structure in 3-manifold topology

Abstract

Let Sigma be a closed oriented surface of genus g. We show that the Kauffman bracket skein module of Sigma x S^1 over the field of rational functions in A has dimension at least 2^{2g+1}+2g-1.