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 finite products of 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.