On cycles and coverings associated to a knot

Lilya Lyubich; Mikhail Lyubich

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arXiv · 1301.2205

On cycles and coverings associated to a knot

Lilya Lyubich·Mikhail Lyubich

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Abstract

We consider the space of all representations of the commutator subgroup of a knot group into a finite abelian group {\Sigma}, together with a shift map {\sigma}_x. This is a finite dynamical system, introduced by D.Silver and S. Williams. We describe the lengths of its cycles in terms of the roots of the Alexander polynomial of the knot. This generalizes our previous result for {\Sigma}= Z/p, p is prime, and gives a complete classification of depth 2 solvable coverings of the knot complement.

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Lilya Lyubich, Mikhail Lyubich. 2013-01-10. On cycles and coverings associated to a knot. https://arxiv.org/abs/1301.2205

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