Year: 2024
Type: preprint
Abstract: This paper uses the renowned Kechris-Pestov-Todorcevic 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.
DOI: 10.1090/proc/17101
Author: Yusen Long
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Chinese Government Scholarship
Award: G238581022
OpenAlex ID: W4404306598