Kauffman Bracket Skein Module of the Connected Sum of Handlebodies: A Counterexample
Geometric Topology
2020-05-19 v1
Abstract
In this paper we disprove a twenty-two year old theorem about the structure of the Kauffman bracket skein module of the connected sum of two handlebodies. We achieve this by analysing handle slidings on compressing discs in a handlebody. We find more relations than previously predicted for the Kauffman bracket skein module of the connected sum of handlebodies, when one of them is not a solid torus. Additionally, we speculate on the structure of the Kauffman bracket skein module of the connected sum of two solid tori.
Keywords
Cite
@article{arxiv.2005.07750,
title = {Kauffman Bracket Skein Module of the Connected Sum of Handlebodies: A Counterexample},
author = {Rhea Palak Bakshi and Józef H. Przytycki},
journal= {arXiv preprint arXiv:2005.07750},
year = {2020}
}
Comments
10 pages, 15 figures