Kauffman Bracket Skein Module of the Connected Sum of Handlebodies: A Counterexample

Rhea Palak Bakshi; Józef H. Przytycki

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arXiv · 2005.07750

Kauffman Bracket Skein Module of the Connected Sum of Handlebodies: A Counterexample

Rhea Palak Bakshi·Józef H. Przytycki

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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.

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BibTeX RIS

Rhea Palak Bakshi, Józef H. Przytycki. 2020-05-15. Kauffman Bracket Skein Module of the Connected Sum of Handlebodies: A Counterexample. https://arxiv.org/abs/2005.07750

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