Virtually free-by-cyclic groups
We obtain a homological characterisation of virtually free-by-cyclic groups among groups that are hyperbolic and virtually compact special. As a consequence, we show that many groups known to be coherent actually possess the stronger property of being virtually free-by-cyclic. In particular, we show...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Springer Nature
2024
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| _version_ | 1811141072854712320 |
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| author | Kielak, D Linton, M |
| author_facet | Kielak, D Linton, M |
| author_sort | Kielak, D |
| collection | OXFORD |
| description | We obtain a homological characterisation of virtually free-by-cyclic groups among groups that are hyperbolic and virtually compact special. As a consequence, we show that many groups known to be coherent actually possess the stronger property of being virtually free-by-cyclic. In particular, we show that all one-relator groups with torsion are virtually free-by-cyclic, solving a conjecture of Baumslag. |
| first_indexed | 2024-09-25T04:32:04Z |
| format | Journal article |
| id | oxford-uuid:882eb631-06af-4174-be3f-1bf210368653 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:32:04Z |
| publishDate | 2024 |
| publisher | Springer Nature |
| record_format | dspace |
| spelling | oxford-uuid:882eb631-06af-4174-be3f-1bf2103686532024-09-02T11:07:30ZVirtually free-by-cyclic groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:882eb631-06af-4174-be3f-1bf210368653EnglishSymplectic ElementsSpringer Nature2024Kielak, DLinton, MWe obtain a homological characterisation of virtually free-by-cyclic groups among groups that are hyperbolic and virtually compact special. As a consequence, we show that many groups known to be coherent actually possess the stronger property of being virtually free-by-cyclic. In particular, we show that all one-relator groups with torsion are virtually free-by-cyclic, solving a conjecture of Baumslag. |
| spellingShingle | Kielak, D Linton, M Virtually free-by-cyclic groups |
| title | Virtually free-by-cyclic groups |
| title_full | Virtually free-by-cyclic groups |
| title_fullStr | Virtually free-by-cyclic groups |
| title_full_unstemmed | Virtually free-by-cyclic groups |
| title_short | Virtually free-by-cyclic groups |
| title_sort | virtually free by cyclic groups |
| work_keys_str_mv | AT kielakd virtuallyfreebycyclicgroups AT lintonm virtuallyfreebycyclicgroups |