Work

Partial Torelli groups and homological stability

Year: 2023

Type: article

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.57K20 Ã

Source: Algebraic & Geometric Topology

DOI: 10.2140/agt.2023.23.3417

Author: Andrew Putman

Institution: University of Notre Dame

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: National Science Foundation

Award: Topology and group theory