Profinite rigidity for twisted Alexander polynomials

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.

19pages; several remarks are inserted (v3), several minor errors are corrected (v4) +3pages; "Erratum" is added at the end (v6)

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