English

Profinite rigidity for twisted Alexander polynomials

Geometric Topology 2021-11-19 v6

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 Z\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.

Keywords

Cite

@article{arxiv.1909.01334,
  title  = {Profinite rigidity for twisted Alexander polynomials},
  author = {Jun Ueki},
  journal= {arXiv preprint arXiv:1909.01334},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-23T11:04:24.628Z