Knot symmetries and the fundamental quandle

Eva Horvat

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arXiv · 1707.04824

Knot symmetries and the fundamental quandle

Eva Horvat

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Abstract

We establish a relationship between the knot symmetries and the automorphisms of the knot quandle. We identify the homeomorphisms of the pair $(S^{3},K)$ that induce the (anti)automorphisms of the fundamental quandle $Q(K)$. We show that every quandle (anti)automorphism of $Q(K)$ is induced by a homeomorphism of the pair $(S^{3},K)$. As an application of those results, we are able to explore some symmetry properties of a knot based on the presentation of its fundamental quandle, which is easily derived from a knot diagram.

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BibTeX RIS

Eva Horvat. 2017-07-16. Knot symmetries and the fundamental quandle. https://arxiv.org/abs/1707.04824

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