Compact and finite-type support in the homology of big mapping class groups
| Autor: | Palmer, Martin, Wu, Xiaolei |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 23 pages, 5 figures. v2: statements of results have been clarified to carefully disambiguate the three distinct questions that we answer. Comments welcome! |
| Databáze: | arXiv |
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