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Representations of knot groups and Vassiliev invariants

Daniel Altschuler
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Abstract

We show that the number of homomorphisms from a knot group to a finite group $G$ cannot be a Vassiliev invariant, unless it is constant on the set of $(2,2p+1)$ torus knots. In several cases, such as when $G$ is a dihedral or symmetric group, this implies that the number of homomorphisms is not a Vassiliev invariant.

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Daniel Altschuler. 1995-03-27. Representations of knot groups and Vassiliev invariants. https://arxiv.org/abs/q-alg/9503015

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