Compact and finite-type support in the homology of big mapping class groups
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908536134434816 |
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| author | Palmer, Martin Wu, Xiaolei |
| author_facet | Palmer, Martin Wu, Xiaolei |
| contents | For any infinite-type surface $S$, a natural question is whether the homology of its mapping class group contains any non-trivial classes that are supported on (i) a compact subsurface or (ii) a finite-type subsurface. Our purpose here is to study this question, in particular giving an almost-complete answer when the genus of $S$ is positive (including infinite) and a partial answer when the genus of $S$ is zero. Our methods involve the notion of shiftable subsurfaces as well as homological stability for mapping class groups of finite-type surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compact and finite-type support in the homology of big mapping class groups Palmer, Martin Wu, Xiaolei Geometric Topology Algebraic Topology Group Theory 57K20, 20J06 For any infinite-type surface $S$, a natural question is whether the homology of its mapping class group contains any non-trivial classes that are supported on (i) a compact subsurface or (ii) a finite-type subsurface. Our purpose here is to study this question, in particular giving an almost-complete answer when the genus of $S$ is positive (including infinite) and a partial answer when the genus of $S$ is zero. Our methods involve the notion of shiftable subsurfaces as well as homological stability for mapping class groups of finite-type surfaces. |
| title | Compact and finite-type support in the homology of big mapping class groups |
| topic | Geometric Topology Algebraic Topology Group Theory 57K20, 20J06 |
| url | https://arxiv.org/abs/2405.03512 |