Mapping class group action on the cohomology of the $\mathrm{SL}_n$ character variety
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912964404051968 |
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| author | Larsen, Anne |
| author_facet | Larsen, Anne |
| contents | We describe the mapping class group action on the cohomology of the twisted $\mathrm{SL}_n$-character variety of a surface $Σ_g$ of genus $g$. Our main tool is a relative version of the endoscopic decomposition of Maulik-Shen; this allows us to reduce the problem to the mapping class group action on the cohomology of a canonical finite cover of $Σ_g$, which was studied by Looijenga. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12484 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mapping class group action on the cohomology of the $\mathrm{SL}_n$ character variety Larsen, Anne Algebraic Geometry Geometric Topology 14D20, 57K20 We describe the mapping class group action on the cohomology of the twisted $\mathrm{SL}_n$-character variety of a surface $Σ_g$ of genus $g$. Our main tool is a relative version of the endoscopic decomposition of Maulik-Shen; this allows us to reduce the problem to the mapping class group action on the cohomology of a canonical finite cover of $Σ_g$, which was studied by Looijenga. |
| title | Mapping class group action on the cohomology of the $\mathrm{SL}_n$ character variety |
| topic | Algebraic Geometry Geometric Topology 14D20, 57K20 |
| url | https://arxiv.org/abs/2603.12484 |