Partial Torelli groups and homological stability

Putman, Andrew

doi:10.2140/agt.2023.23.3417

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Partial Torelli groups and homological stability

Andrew Putman

Algebraic & Geometric Topology 23 (2023) 3417–3496

DOI: 10.2140/agt.2023.23.3417

Abstract

We prove a homological stability theorem for the subgroup of the mapping class group acting as the identity on some fixed portion of the first homology group of the surface. We also prove a similar theorem for the subgroup of the mapping class group preserving a fixed map from the fundamental group to a finite group, which can be viewed as a mapping class group version of a theorem of Ellenberg, Venkatesh and Westerland about braid groups. These results require studying various simplicial complexes formed by subsurfaces of the surface, generalizing work of Hatcher and Vogtmann.

Keywords

mapping class group, Torelli group, homological stability

Mathematical Subject Classification

Primary: 57K20

References

Publication

Received: 29 May 2020

Revised: 18 April 2022

Accepted: 26 June 2022

Published: 5 November 2023

Authors

Andrew Putman
Department of Mathematics University of Notre Dame Notre Dame, IN United States

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Volume 23, issue 8 (2023)