Skein module dimensions of mapping tori of the 2-torus

2023/04/14 by Kinnear, Patrick · 2 citations
#16E40 (Secondary) #57K16 #57K31 #57R22 #57R56 (Primary) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2304.07332

Abstract

We determine the dimension of the Kauffman bracket skein module at generic q for mapping tori of the 2-torus, generalising the well-known computation of Carrega and Gilmer. In the process, we give a decomposition of the twisted Hochschild homology of the G-skein algebra for G = SL_N or GL_N, which is a direct summand of the whole skein module, and from which the dimensions follow easily in the cases G = SL₂ and G = GL₁.

Cited by

• The skein partition function of the mapping torus
• SL_N Quantum-Torus Summands and Visible Nielsen Numbers

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