On the Kauffman bracket skein module of surgery on a (2,2b) torus link

TL;DR

This paper investigates the structure of the Kauffman bracket skein modules of 3-manifolds resulting from integral surgeries on (2,2b) torus links, demonstrating finite generation and providing explicit generators for specific cases.

Contribution

It establishes finite generation of these skein modules and explicitly lists generators for particular examples, advancing understanding of their algebraic structure.

Findings

Kauffman bracket skein modules are finitely generated after surgery on (2,2b) links

Explicit generators are identified for select manifold examples

Provides a foundation for further algebraic and topological analysis of these modules

Abstract

We show that the Kauffman bracket skein modules of certain manifolds obtained from integral surgery on a (2,2b) torus link are finitely generated, and list the generators for select examples.