2020/05/15 by Rhea Palak Bakshi, Bakshi, Rhea Palak, Józef H. Przytycki +1
Mathematics · #57K10 #57K31 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57K10 #msc:57K31
paper · pdf · doi:10.48550/arxiv.2005.07750
10 pages, 15 figures
arxiv created 2020/05/15 · arxiv updated 2020/05/19
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.