The Kauffman skein module of the connected sum of 3-manifolds

2002/05/13 by Jianyuan K. Zhong, Zhong, Jianyuan K.
Mathematics · #57M #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:57M

paper · pdf · doi:10.48550/arxiv.math/0205131

15 pages, 41 figures, amslatex, using epsf.tex

openalex publication_date 2002/05/13 · arxiv created 2002/10/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be an integral domain containing the invertible elements α, s and \frac1s-s^-1. If M is an oriented 3-manifold, let K(M) denote the Kauffman skein module of M over k. Based on the work on Birman-Murakami-Wenzl algebra by Beliakova and Blanchet, we give an ``idempotent-like'' basis for the Kauffman skein module of handlebodies. Gilmer and Zhong have studied the Homflypt skein modules of a connected sum of two 3-manifolds, here we study the case for the Kauffman skein module and show that K(M₁ # M₂) is isomorphic to K(M₁) tensor K(M₂) over a certain localized ring, where M₁ # M₂ is the connected sum of two manifolds M₁ and M₂.

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