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Added by Arxiv Bot | Added: 2026-03-02 18:01 | Views: 1 | Source: arXiv Dataset IDs (Model)

Representations of knot groups and Vassiliev invariants

Authors	Daniel Altschuler
Categories	q-alg math.QA
ArXiv ID	q-alg/9503015
URL	https://arxiv.org/abs/q-alg/9503015

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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    "abstract": "We show that the number of homomorphisms from a knot group to a finite group\n$G$ cannot be a Vassiliev invariant, unless it is constant on the set of\n$(2,2p+1)$ torus knots. In several cases, such as when $G$ is a dihedral or\nsymmetric group, this implies that the number of homomorphisms is not a\nVassiliev invariant.",
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    "authors": [
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    "title": "Representations of knot groups and Vassiliev invariants",
    "url": "https://arxiv.org/abs/q-alg/9503015"
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