A Counterexample to the Generalisation of Witten's Conjecture

TL;DR

This paper presents a counterexample that challenges the general validity of Witten's conjecture regarding the structure of the Kauffman bracket skein module for certain 3-manifolds.

Contribution

It provides the first known counterexample to Marché's conjecture, demonstrating limitations in the conjecture's applicability.

Findings

Counterexample disproves the conjecture

Limits the conjecture's applicability to certain 3-manifolds

Highlights need for revised understanding of skein modules

Abstract

This note provides a counterexample to a conjecture by March\'e about the structure of the Kauffman bracket skein module for closed compact oriented 3-manifolds over the ring of Laurent polynomials.