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

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• 作者：Zhong ; Jianyuan K.
• 关键词：57M ; Skein modules ; Birman&ndash ; Murakami&ndash ; Wenzl algebras ; Connected sum
• 刊名：Topology and its Applications
• 出版年：2004
• 期刊代码：60_01668641
• 类别：mt
• 出版时间：April 28, 2004
• 卷：139
• 期：1-3
• 页码：113-128
• 文件大小：284 K

摘要

Let k be an integral domain containing the invertible elements α, s and . Let M be a compact 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 [Math. Ann. 321 (2001) 347], we give an “idempotent-like” basis for the Kauffman skein module of handlebodies. We study the Kauffman skein module of a connected sum of two 3-manifolds M₁ and M₂ and prove 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.