Quasi-convex Splittings of Acylindrical Graphs of Locally Finite-Height Groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909991215038464 |
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| author | Cohen, William D. |
| author_facet | Cohen, William D. |
| contents | We find a condition on the acylindrical action of a finitely presented group on a simplicial tree which guarantees that this action will be dominated by an acylindrical action with finitely generated edge stabilisers, and find the first example of an action of a finitely presented group where there is no such dominating action. As a consequence, we show that any finitely presented group that admits a decomposition as an acylindrical graph of (possibly infinitely generated) free groups is virtually compact special, and that every finitely generated subgroup of a one-relator group with an acylindrical Magnus hierarchy is virtually compact special. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_15459 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-convex Splittings of Acylindrical Graphs of Locally Finite-Height Groups Cohen, William D. Group Theory 20E08 (Primary), 20F65 (Secondary), 20F67 (Secondary) We find a condition on the acylindrical action of a finitely presented group on a simplicial tree which guarantees that this action will be dominated by an acylindrical action with finitely generated edge stabilisers, and find the first example of an action of a finitely presented group where there is no such dominating action. As a consequence, we show that any finitely presented group that admits a decomposition as an acylindrical graph of (possibly infinitely generated) free groups is virtually compact special, and that every finitely generated subgroup of a one-relator group with an acylindrical Magnus hierarchy is virtually compact special. |
| title | Quasi-convex Splittings of Acylindrical Graphs of Locally Finite-Height Groups |
| topic | Group Theory 20E08 (Primary), 20F65 (Secondary), 20F67 (Secondary) |
| url | https://arxiv.org/abs/2503.15459 |