Stable orbit equivalence of Bernoulli shifts over free groups

Abstract

Previous work showed that every pair of nontrivial Bernoulli shifts over a fixed free group are orbit equivalent. In this paper, we prove that if $G_1,G_2$ are nonabelian free groups of finite rank then every nontrivial Bernoulli shift over $G_1$ is stably orbit equivalent to every nontrivial Bernoulli shift over $G_2$. This answers a question of S. Popa.

The second version has minor notational changes

References in corpus (3)

• Orbit inequivalent actions of non-amenable groups
• A survey of Measured Group Theory
• Orbit equivalence, coinduced actions and free products