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Skein modules and character varieties Clay, Adam Joseph

Abstract

We present a survey of the theory of skein modules of manifolds, and an introduction to skein algebras of groups. By applying a trick of Doug Bullock, we use SL(2, C) character varieties to highlight some infinite linearly independent families of knots in the Kauffman Bracket skein module of a 3-manifold. These families are composed of a knot K, together with all (1, n)-cablings of K. We also exhibit a method of explicit computation based upon the work of Robert Riley, which can identify infinite linearly independent families in the skein algebras of 2-bridge knot groups.

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