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Cluster C*-algebras and knot polynomials (1603.01180v1)
Published 3 Mar 2016 in math.OA, math.GT, and math.RT
Abstract: We construct a representation of the braid groups in a cluster C*-algebra coming from a triangulation of the Riemann surface S with one or two cusps. It is shown that the Laurent polynomials attached to the K-theory of such an algebra are topological invariants of the closure of braids. In particular, the Jones and HOMFLY polynomials of a knot correspond to the case S being a sphere with two cusps and a torus with one cusp, respectively.
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