The space of stable weak equivalence classes of measure-preserving actions |
| |
Authors: | Lewis Bowen Robin Tucker-Drob |
| |
Abstract: | The concept of (stable) weak containment for measure-preserving actions of a countable group Γ is analogous to the classical notion of (stable) weak containment of unitary representations. If Γ is amenable then the Rokhlin lemma shows that all essentially free actions are weakly equivalent. However if Γ 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 this simplex has only a countable set of extreme points but when Γ is a nonamenable free group, this simplex is the Poulsen simplex. We also show that when Γ contains a nonabelian free group, this simplex has uncountably many strongly ergodic essentially free extreme points. |
| |
Keywords: | 37A35 Weak containment Pmp actions |
本文献已被 ScienceDirect 等数据库收录! |