Homogeneous actions on Urysohn spaces
Group Theory
2021-01-20 v2 Dynamical Systems
Abstract
We show that many countable groups acting on trees, including free products of infinite countable groups and surface groups, are isomorphic to dense subgroups of isometry groups of bounded Urysohn spaces. This extends previous results of the first and last author with Y. Stalder on dense subgroups of the automorphism group of the random graph. In the unbounded case, we also show that every free product of infinite countable groups arises as a dense subgroup of the isometry group of the rational Urysohn space.
Keywords
Cite
@article{arxiv.1805.02477,
title = {Homogeneous actions on Urysohn spaces},
author = {Pierre Fima and François Le Maître and Julien Melleray and Soyoung Moon},
journal= {arXiv preprint arXiv:1805.02477},
year = {2021}
}
Comments
Final version, to appear in Colloquium Mathematicum