Profinite rigidity for twisted Alexander polynomials

Jun Ueki

doi:10.1515/crelle-2020-0014

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arXiv · 1909.01334

Profinite rigidity for twisted Alexander polynomials

Jun Ueki

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Abstract

We formulate and prove a profinite rigidity theorem for the twisted Alexander polynomials up to several types of finite ambiguity. We also establish torsion growth formulas of the twisted homology groups in a $\mathbb{Z}$-cover of a 3-manifold with use of Mahler measures. We examine several examples associated to Riley's parabolic representations of two-bridge knot groups and give a remark on hyperbolic volumes.

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Jun Ueki. 2019-09-03. Profinite rigidity for twisted Alexander polynomials. https://doi.org/10.1515/crelle-2020-0014

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