Twisted Alexander Polynomials and Representation Shifts

Details Twisted Alexander Polynomials and Representation Shifts Twisted Alexander Polynomials and Representation Shifts

2007-08-28

arxiv.org/abs/0708.3831v1

Mathematics

Geometric Topology

7 pages, no figures

Scientific paper

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.

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