Big mapping class groups are not extremely amenable
Geometric Topology
2024-09-24 v3 Group Theory
Abstract
This paper uses the renowned Kechris-Pestov-Todor\v{c}evi\'{c} machinery to show that (big) mapping class groups are not extremely amenable unless the underlying surface is a sphere or a once-punctured sphere, or equivalently when the mapping class group is trivial. The same techniques also show that the pure mapping class groups, as well as compactly supported mapping class groups, of a surface with genus at least one can never be extremely amenable.
Cite
@article{arxiv.2307.12408,
title = {Big mapping class groups are not extremely amenable},
author = {Yusen Long},
journal= {arXiv preprint arXiv:2307.12408},
year = {2024}
}
Comments
9 pages, 1 figure. To appear on Proceedings Of The American Mathematical Society