Partial Torelli groups and homological stability

Andrew Putman

doi:10.2140/agt.2023.23.3417

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arXiv · 1901.06624

Partial Torelli groups and homological stability

Andrew Putman

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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-Westerland about braid groups. These results require studying various simplicial complexes formed by subsurfaces of the surface, generalizing work of Hatcher-Vogtmann.

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Andrew Putman. 2019-01-20. Partial Torelli groups and homological stability. https://doi.org/10.2140/agt.2023.23.3417

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