Profinite rigidity of fibring

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 ${\mathsf{TAP}}_1(R)$ for every integral domain $R$, 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.

30 pages, updated with the referee's comments. To appear in Revista Matemática Iberoamericana

Cited by in corpus (1)

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