Profinite rigidity of fibring
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 TAP1(R) for every integral domain R, and deduce that algebraic fibri...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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European Mathematical Society Press
2025
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| _version_ | 1826317333536178176 |
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| author | Hughes, S Kielak, D |
| author_facet | Hughes, S Kielak, D |
| author_sort | Hughes, S |
| collection | OXFORD |
| description | 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 TAP1(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. |
| first_indexed | 2024-12-09T03:19:05Z |
| format | Journal article |
| id | oxford-uuid:bc7bce47-6f7c-4476-b29e-a6a62454d527 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-02-19T04:38:24Z |
| publishDate | 2025 |
| publisher | European Mathematical Society Press |
| record_format | dspace |
| spelling | oxford-uuid:bc7bce47-6f7c-4476-b29e-a6a62454d5272025-02-07T10:28:33ZProfinite rigidity of fibringJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bc7bce47-6f7c-4476-b29e-a6a62454d527EnglishSymplectic ElementsEuropean Mathematical Society Press2025Hughes, SKielak, DWe 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 TAP1(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. |
| spellingShingle | Hughes, S Kielak, D Profinite rigidity of fibring |
| title | Profinite rigidity of fibring |
| title_full | Profinite rigidity of fibring |
| title_fullStr | Profinite rigidity of fibring |
| title_full_unstemmed | Profinite rigidity of fibring |
| title_short | Profinite rigidity of fibring |
| title_sort | profinite rigidity of fibring |
| work_keys_str_mv | AT hughess profiniterigidityoffibring AT kielakd profiniterigidityoffibring |