Twisted Alexander Polynomials and Representation Shifts

Daniel S. Silver; Susan G. Williams

doi:10.1112/blms/bdp029

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arXiv · 0708.3831

Twisted Alexander Polynomials and Representation Shifts

Daniel S. Silver·Susan G. Williams

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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.

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Daniel S. Silver, Susan G. Williams. 2007-08-28. Twisted Alexander Polynomials and Representation Shifts. https://doi.org/10.1112/blms%2Fbdp029

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