The Kauffman Skein Module of the Connected Sum of 3-manifolds
نویسنده
چکیده
Let k be an integral domain containing the invertible elements α, s and 1 s−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 [2], we give an “idempotent-like” basis for the Kauffman skein module of handlebodies. Gilmer and Zhong [6] 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)⊗K(M2) over a certain localized ring, where M1#M2 is the connected sum of two manifolds M1 and M2.
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