Farrell cohomology of the pure mapping class group of non-orientable surfaces
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912083448168448 |
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| author | Colin, Nestor |
| author_facet | Colin, Nestor |
| contents | For an odd prime $p$, we determine the $p$-primary component of the Farrell cohomology of the pure mapping class groups of a non orientable surface of genus $p$ with $k\geqslant 1$ marked points. To do this, we classify conjugacy classes of subgroups of order $p$ of the pure mapping class group of a non orientable surface of any genus with marked points. This is obtained by extending the notion of topological equivalence for surface kernel epimorphisms of non Euclidean crystallographic groups, adapting it to the setting of surfaces with marked points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17977 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Farrell cohomology of the pure mapping class group of non-orientable surfaces Colin, Nestor Geometric Topology Algebraic Topology Primary 57K20, 55N20, 55N35, 57M07, 57M60, Secondary 57S05, 20H10 For an odd prime $p$, we determine the $p$-primary component of the Farrell cohomology of the pure mapping class groups of a non orientable surface of genus $p$ with $k\geqslant 1$ marked points. To do this, we classify conjugacy classes of subgroups of order $p$ of the pure mapping class group of a non orientable surface of any genus with marked points. This is obtained by extending the notion of topological equivalence for surface kernel epimorphisms of non Euclidean crystallographic groups, adapting it to the setting of surfaces with marked points. |
| title | Farrell cohomology of the pure mapping class group of non-orientable surfaces |
| topic | Geometric Topology Algebraic Topology Primary 57K20, 55N20, 55N35, 57M07, 57M60, Secondary 57S05, 20H10 |
| url | https://arxiv.org/abs/2410.17977 |