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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- 10.48550/arXiv.2206.11347
- arXiv:
- arXiv:2206.11347
- Bibcode:
- 2022arXiv220611347H
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Geometric Topology;
- 20J05;
- 20E18;
- 20F67
- E-Print:
- 34 pages