Cost of inner amenable groupoids
Dynamical Systems
2021-02-05 v4 Group Theory
Logic
Operator Algebras
Abstract
Kida and Tucker-Drob recently extended the notion of inner amenability from countable groups to discrete p.m.p. groupoids. In this article, we show that inner amenable groupoids have "fixed priced 1" in the sense that every principal extension of an inner amenable groupoid has cost 1. This simultaneously generalizes and unifies two well known results on cost from the literature, namely, (1) a theorem of Kechris stating that every ergodic p.m.p. equivalence relation admitting a nontrivial asymptotically central sequence in its full group has cost 1, and (2) a theorem of Tucker-Drob stating that inner amenable groups have fixed price 1.
Keywords
Cite
@article{arxiv.2009.11108,
title = {Cost of inner amenable groupoids},
author = {Robin Tucker-Drob and Konrad Wróbel},
journal= {arXiv preprint arXiv:2009.11108},
year = {2021}
}
Comments
Incorporates referee comments. To appear in Proceedings of the AMS