Orbit equivalence, coinduced actions and free products

Abstract

The following result is proven. Let $G_1 \cc^{T_1} (X_1,μ_1)$ and $G_2 \cc^{T_2} (X_2,μ_2)$ be orbit-equivalent, essentially free, probability measure preserving actions of countable groups $G_1$ and $G_2$. Let $H$ be any countable group. For $i=1,2$, let ${\Gamma }_i=G_i\ast H$ be the free product. Then the actions of ${\Gamma }_1$ and ${\Gamma }_2$ coinduced from $T_1$ and $T_2$ are orbit-equivalent. As an application, it is shown that if $\Gamma$ is a free group, then all nontrivial Bernoulli shifts over $\Gamma$ are orbit-equivalent.

New version. The cocycles have been standardized and proofs simplified. A reference has been corrected.

References in corpus (3)

• Orbit inequivalent actions of non-amenable groups
• A survey of Measured Group Theory
• Orbit inequivalent actions for groups containing a copy of ${\mathbb{F}}_2$

Cited by in corpus (1)

• Stable orbit equivalence of Bernoulli shifts over free groups