Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896669 | Journal of Functional Analysis | 2018 | 27 Pages |
Abstract
The concept of (stable) weak containment for measure-preserving actions of a countable group Î is analogous to the classical notion of (stable) weak containment of unitary representations. If Î is amenable then the Rokhlin lemma shows that all essentially free actions are weakly equivalent. However if Î is non-amenable then there can be many different weak and stable weak equivalence classes. Our main result is that the set of stable weak equivalence classes naturally admits the structure of a Choquet simplex. For example, when Î=Z this simplex has only a countable set of extreme points but when Î is a nonamenable free group, this simplex is the Poulsen simplex. We also show that when Î contains a nonabelian free group, this simplex has uncountably many strongly ergodic essentially free extreme points.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Lewis Bowen, Robin Tucker-Drob,