The Kauffman bracket skein module of two-bridge links

TL;DR

This paper computes the Kauffman bracket skein module of two-bridge link complements, revealing its algebraic structure and connection to the character variety, thus advancing understanding of link invariants.

Contribution

It provides an explicit calculation of the KBSM for all two-bridge links and establishes its isomorphism with the ring of regular functions on the character variety.

Findings

KBSM of two-bridge link complements is free over $c[t^{pm 1}]$

Reduction at t=-1 yields the character variety's coordinate ring

The results unify skein modules with character varieties for these links

Abstract

We calculate the Kauffman bracket skein module (KBSM) of the complement of all two-bridge links. For a two-bridge link, we show that the KBSM of its complement is free over the ring $\BC[t^{\pm 1}]$ and when reducing $t=-1$, it is isomorphic to the ring of regular functions on the character variety of the link group.