Profinite rigidity of fibring
Sam Hughes
University of Oxford, Oxford, UK; Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, GermanyDawid Kielak
University of Oxford, Oxford, UK
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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 finite products of 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 Poincaré duality groups in dimension 3 and RFRS groups.
Cite this article
Sam Hughes, Dawid Kielak, Profinite rigidity of fibring. Rev. Mat. Iberoam. (2025), published online first
DOI 10.4171/RMI/1524