Stable commutator length on big mapping class groups
Geometric Topology
2022-06-13 v3 Group Theory
Abstract
We study stable commutator length on mapping class groups of certain infinite-type surfaces. In particular, we show that stable commutator length defines a continuous function on the commutator subgroups of such infinite-type mapping class groups. We furthermore show that the commutator subgroups are open and closed subgroups and that the abelianizations are finitely generated in many cases. Our results apply to many popular infinite-type surfaces with locally coarsely bounded mapping class groups.
Cite
@article{arxiv.2108.02123,
title = {Stable commutator length on big mapping class groups},
author = {Elizabeth Field and Priyam Patel and Alexander J. Rasmussen},
journal= {arXiv preprint arXiv:2108.02123},
year = {2022}
}
Comments
Final version to appear in Bulletin of the London Mathematical Society