Extensions of amenable groups by recurrent groupoids
Group Theory
2017-10-05 v2 Functional Analysis
Probability
Abstract
We show that amenability of a group acting by homeomorphisms can be deduced from a certain local property of the action and recurrency of the orbital Schreier graphs. This covers amenability of a wide class groups, the amenability of which was an open problem, as well as unifies many known examples to one general proof. In particular, this includes Grigorchuk's group, Basilica group, the full topological group of Cantor minimal system, groups acting on rooted trees by bounded automorphisms, groups generated by finite automata of linear activity growth, groups that naturally appear in holomorphic dynamics.
Cite
@article{arxiv.1305.2637,
title = {Extensions of amenable groups by recurrent groupoids},
author = {Kate Juschenko and Volodymyr Nekrashevych and Mikael de la Salle},
journal= {arXiv preprint arXiv:1305.2637},
year = {2017}
}
Comments
The last condition of the main thm was removed, the proofs are streamlined