Non-amenability of mapping class groups of infinite-type surfaces and graphs
Group Theory
2026-03-10 v3 Geometric Topology
Abstract
This paper completely determines the non-amenability of the mapping class groups of infinite-type surfaces, the mapping class groups of locally finite infinite graphs of higher ranks, gives an example of non-amenable stabiliser of a point at infinity of a coarsely bounded generated hyperbolic Polish group, and exhibits a class of mapping class groups of trees or rank-one graphs that are amenable.
Keywords
Cite
@article{arxiv.2506.06538,
title = {Non-amenability of mapping class groups of infinite-type surfaces and graphs},
author = {Yusen Long},
journal= {arXiv preprint arXiv:2506.06538},
year = {2026}
}
Comments
v3. To appear on Bull. Lond. Math. Soc