Asymptotically rigid mapping class groups III: Presentations and isomorphisms
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912644708958208 |
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| author | Genevois, Anthony Lonjou, Anne Urech, Christian |
| author_facet | Genevois, Anthony Lonjou, Anne Urech, Christian |
| contents | This article is dedicated to the computation of an explicit presentation of some asymptotically rigid mapping class groups, namely the braided Higman-Thompson groups. To do so, we use the action of these groups on the spine complex, a simply connected cube complex constructed by the authors in a previous work. In particular, this allows to compute the abelianisations of these groups. With these new algebraic invariants we can handle many new cases of the isomorphism problem for asymptotically rigid mapping class groups of trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11336 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotically rigid mapping class groups III: Presentations and isomorphisms Genevois, Anthony Lonjou, Anne Urech, Christian Group Theory 20F65, 20F05 This article is dedicated to the computation of an explicit presentation of some asymptotically rigid mapping class groups, namely the braided Higman-Thompson groups. To do so, we use the action of these groups on the spine complex, a simply connected cube complex constructed by the authors in a previous work. In particular, this allows to compute the abelianisations of these groups. With these new algebraic invariants we can handle many new cases of the isomorphism problem for asymptotically rigid mapping class groups of trees. |
| title | Asymptotically rigid mapping class groups III: Presentations and isomorphisms |
| topic | Group Theory 20F65, 20F05 |
| url | https://arxiv.org/abs/2510.11336 |