Arithmetic representations of mapping class groups

Eduard Looijenga

doi:10.2140/agt.2025.25.677

Arithmetic representations of mapping class groups

Geometric Topology 2025-05-21 v3 Algebraic Geometry Group Theory

Authors: Eduard Looijenga

View on arXiv ↗ PDF ↗ DOI ↗

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).

Keywords

mapping class groups of surfaces mapping class groups automorphism groups

Cite

@article{arxiv.2108.12791,
  title  = {Arithmetic representations of mapping class groups},
  author = {Eduard Looijenga},
  journal= {arXiv preprint arXiv:2108.12791},
  year   = {2025}
}

Comments

Minor corrections and improved presentation, to appear in Algebraic & Geometric Topology. 19p

Arithmetic representations of mapping class groups

Abstract

Keywords

Cite

Comments

Related papers