Profinite rigidity of fibring
Group Theory
2026-03-03 v2 Geometric Topology
Abstract
We introduce the classes of TAP groups, in which various types of algebraic fibring are detected by the non-vanishing of twisted Alexander polynomials. We show that finitely presented LERF groups lie in the class for every integral domain , and deduce that algebraic fibring is a profinite property for such groups. We offer stronger results for algebraic fibring of products of limit groups, as well as applications to profinite rigidity of Poincar\'e duality groups in dimension and RFRS groups.
Cite
@article{arxiv.2206.11347,
title = {Profinite rigidity of fibring},
author = {Sam Hughes and Dawid Kielak},
journal= {arXiv preprint arXiv:2206.11347},
year = {2026}
}
Comments
30 pages, updated with the referee's comments. To appear in Revista Matem\'atica Iberoamericana