PSL(2,C) Representations of Knot Groups

Kate Petersen (University of Minnesota Duluth)

I will discuss a method of producing defining equations for representation varieties of the canonical component of a knot group into PSL(2,C). This method uses only a knot diagram satisfying a mild restriction and is based upon the underlying geometry of the knot complement. In particular, it does not involve any polyhedral decomposition or triangulation of the link complement. This results in a simple algorithm that can often be performed by hand, and in many cases, for an infinite family of knots at once. This is joint work with Anastasiia Tsvietkova.

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