Profinite rigidity of fibring
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911476635140096 |
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| author | Hughes, Sam Kielak, Dawid |
| author_facet | Hughes, Sam Kielak, Dawid |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_11347 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Profinite rigidity of fibring Hughes, Sam Kielak, Dawid Group Theory Geometric Topology 20J05, 20E18, 20F67 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. |
| title | Profinite rigidity of fibring |
| topic | Group Theory Geometric Topology 20J05, 20E18, 20F67 |
| url | https://arxiv.org/abs/2206.11347 |