On cycles and coverings associated to a knot
Geometric Topology
2013-01-11 v1 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1301.2205,
title = {On cycles and coverings associated to a knot},
author = {Lilya Lyubich and Mikhail Lyubich},
journal= {arXiv preprint arXiv:1301.2205},
year = {2013}
}