Arithmetic representations of mapping class groups

Looijenga, Eduard

doi:10.2140/agt.2025.25.677

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Arithmetic representations of mapping class groups

Eduard Looijenga

Algebraic & Geometric Topology 25 (2025) 677–698

DOI: 10.2140/agt.2025.25.677

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 two. 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.

Keywords

mapping class group, arithmetic representation, arithmetic group

Mathematical Subject Classification

Primary: 57K20, 57M12

Secondary: 11E39

References

Publication

Received: 2 September 2021

Revised: 21 September 2023

Accepted: 8 October 2023

Published: 16 May 2025

Authors

Eduard Looijenga
Mathematics Department University of Chicago Chicago, IL United States	Mathematisch Instituut Universiteit Utrecht Utrecht Netherlands

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Volume 25, issue 2 (2025)