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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2106.08751 |
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| _version_ | 1866909922949595136 |
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| author | Skipper, Rachel Wu, Xiaolei |
| author_facet | Skipper, Rachel Wu, Xiaolei |
| contents | We generalize the notion of asymptotic mapping class groups and allow them to surject to the Higman--Thompson groups, answering a question of Aramayona and Vlamis in the case of the Higman--Thompson groups. When the underlying surface is a disk, these new asymptotic mapping class groups can be identified with the ribbon and oriented ribbon Higman--Thompson groups. We use this model to prove that the ribbon Higman--Thompson groups satisfy homological stability, providing the first homological stability result for dense subgroups of big mapping class groups. Our result can also be treated as an extension of Szymik--Wahl's work on homological stability for the Higman--Thompson groups to the surface setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_08751 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Homological stability for the ribbon Higman--Thompson groups Skipper, Rachel Wu, Xiaolei Group Theory Algebraic Topology K-Theory and Homology 20F36, 57M07, 19D23, 20J05 We generalize the notion of asymptotic mapping class groups and allow them to surject to the Higman--Thompson groups, answering a question of Aramayona and Vlamis in the case of the Higman--Thompson groups. When the underlying surface is a disk, these new asymptotic mapping class groups can be identified with the ribbon and oriented ribbon Higman--Thompson groups. We use this model to prove that the ribbon Higman--Thompson groups satisfy homological stability, providing the first homological stability result for dense subgroups of big mapping class groups. Our result can also be treated as an extension of Szymik--Wahl's work on homological stability for the Higman--Thompson groups to the surface setting. |
| title | Homological stability for the ribbon Higman--Thompson groups |
| topic | Group Theory Algebraic Topology K-Theory and Homology 20F36, 57M07, 19D23, 20J05 |
| url | https://arxiv.org/abs/2106.08751 |