Big mapping class groups acting on homology

TL;DR

This paper investigates how large mapping class groups act on the first homology of surfaces, providing a detailed description of the image of the associated homology representation.

Contribution

It offers a precise characterization of the image of the homology representation induced by big mapping class groups, advancing understanding of their algebraic actions.

Findings

Explicit description of the homology representation image

New insights into the algebraic structure of big mapping class groups

Enhanced understanding of surface automorphisms on homology

Abstract

We study the action of (big) mapping class groups on the first homology of the corresponding surface. We give a precise characterization of the image of the induced homology representation.