Abstract.
Let k be a subring of the field of rational functions in α, s which contains α ±1 ,s ±1. Let M be a compact oriented 3-manifold, and let K(M) denote the Kauffman skein module of M over k. Then K(M) is the k-module freely generated by isotopy classes of framed links in M modulo the Kauffman skein relations. In the case of , the field of rational functions in α, s, we give a basis for the Kauffman skein module of the solid torus and a basis for the relative Kauffman skein module of the solid torus with two points on the boundary. We then show that K(S 1 × S 2 is freely generated by the empty link, i.e., .
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Received: 20 October 2001 / Revised version: 20 March 2002
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Zhong, J., Lu, B. On the Kauffman skein modules. Manuscripta Math. 109, 29–47 (2002). https://doi.org/10.1007/s002290200284
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DOI: https://doi.org/10.1007/s002290200284