Generating sets for the Kauffman skein module of a family of Seifert fibered spaces

TL;DR

This paper investigates the structure of the Kauffman bracket skein module for certain Seifert fibered spaces, demonstrating that it is finitely generated over its boundary skein algebra, which advances understanding of these topological invariants.

Contribution

It provides explicit generating sets for the Kauffman skein modules of orientable Seifert fibered spaces with boundary, showing their finite generation over boundary skein algebras.

Findings

KBSM is finitely generated over boundary skein algebra

Explicit spanning sets for KBSM of Seifert fibered spaces

Enhanced understanding of skein modules in 3-manifold topology

Abstract

We study spanning sets for the Kauffman bracket skein module $\mathcal{S}(M,\mathbb{Q}(A))$ of orientable Seifert fibered spaces with orientable base and non-empty boundary. As a consequence, we show that the KBSM of such manifolds is a finitely generated $\mathcal{S}(\partial M, \mathbb{Q}(A))$-module.