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arXiv · 2603.12484

Mapping class group action on the cohomology of the $\mathrm{SL}_n$ character variety

Anne Larsen
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Abstract

We describe the mapping class group action on the cohomology of the twisted $\mathrm{SL}_n$-character variety of a surface $\Sigma_g$ 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 $\Sigma_g$, which was studied by Looijenga.

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Anne Larsen. 2026-03-12. Mapping class group action on the cohomology of the $\mathrm{SL}_n$ character variety. https://arxiv.org/abs/2603.12484

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