Twisted Alexander Polynomials and Representation Shifts
Geometric Topology
2014-02-26 v1
Abstract
For any knot, the following are equivalent. (1) The infinite cyclic cover has uncountably many finite covers; (2) there exists a finite-image representation of the knot group for which the twisted Alexander polynomial vanishes; (3) the knot group admits a finite-image representation such that the image of the fundamental group of an incompressible Seifert surface is a proper subgroup of the image of the commutator subgroup of the knot group.
Cite
@article{arxiv.0708.3831,
title = {Twisted Alexander Polynomials and Representation Shifts},
author = {Daniel S. Silver and Susan G. Williams},
journal= {arXiv preprint arXiv:0708.3831},
year = {2014}
}
Comments
7 pages, no figures