A combination theorem for hierarchically quasiconvex subgroups, and application to geometric subgroups of mapping class groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912804890476544 |
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| author | Mangioni, Giorgio |
| author_facet | Mangioni, Giorgio |
| contents | We provide sufficient conditions for two subgroups of a hierarchically hyperbolic group to generate an amalgamated free product over their intersection. The result applies in particular to certain geometric subgroups of mapping class groups of finite-type surfaces, that is, those subgroups coming from the embeddings of closed subsurfaces. In the second half of the paper, we study under which hypotheses our amalgamation procedure preserves several notions of convexity, such as hierarchical quasiconvexity (as introduced by Behrstock, Hagen, and Sisto) and strong quasiconvexity (every quasigeodesic with endpoints on the subset lies in a uniform neighbourhood). This answers a question of Russell, Spriano, and Tran. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03602 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A combination theorem for hierarchically quasiconvex subgroups, and application to geometric subgroups of mapping class groups Mangioni, Giorgio Group Theory Geometric Topology 20F65 (Primary) 57K20, 51F30 (Secondary) We provide sufficient conditions for two subgroups of a hierarchically hyperbolic group to generate an amalgamated free product over their intersection. The result applies in particular to certain geometric subgroups of mapping class groups of finite-type surfaces, that is, those subgroups coming from the embeddings of closed subsurfaces. In the second half of the paper, we study under which hypotheses our amalgamation procedure preserves several notions of convexity, such as hierarchical quasiconvexity (as introduced by Behrstock, Hagen, and Sisto) and strong quasiconvexity (every quasigeodesic with endpoints on the subset lies in a uniform neighbourhood). This answers a question of Russell, Spriano, and Tran. |
| title | A combination theorem for hierarchically quasiconvex subgroups, and application to geometric subgroups of mapping class groups |
| topic | Group Theory Geometric Topology 20F65 (Primary) 57K20, 51F30 (Secondary) |
| url | https://arxiv.org/abs/2409.03602 |