Arithmetic representations of mapping class groups

Eduard Looijenga

doi:10.2140/agt.2025.25.677

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arXiv · 2108.12791

Arithmetic representations of mapping class groups

Eduard Looijenga

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Abstract

Let $S$ be a closed oriented surface and $G$ a finite group of orientation preserving automorphisms of $S$ whose orbit space has genus at least $2$. There is a natural group homomorphism from the $G$-centralizer in $Diff^+(S)$ to the $G$-centralizer in $Sp(H_1(S))$. We give a sufficient condition for its image to be a subgroup of finite index and a weaker condition for this to have no finite nonzero orbit (the Putman-Wieland property).

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Eduard Looijenga. 2021-08-29. Arithmetic representations of mapping class groups. https://doi.org/10.2140/agt.2025.25.677

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