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arXiv · 2206.11347

Profinite rigidity of fibring

Sam Hughes·Dawid Kielak
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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 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.

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Sam Hughes, Dawid Kielak. 2024-10-29. Profinite rigidity of fibring. https://doi.org/10.4171/rmi%2F1524

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