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Partial Torelli groups and homological stability

Andrew Putman

Algebraic & Geometric Topology 23 (2023) 3417–3496
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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