Stable orbit equivalence of Bernoulli shifts over free groups

TL;DR

This paper proves that Bernoulli shifts over different nonabelian free groups of finite rank are stably orbit equivalent, extending previous results and answering a question posed by S. Popa.

Contribution

It establishes stable orbit equivalence between Bernoulli shifts over different nonabelian free groups of finite rank, generalizing prior work on orbit equivalence.

Findings

Bernoulli shifts over different free groups are stably orbit equivalent

Answers a question of S. Popa about orbit equivalence

Extends previous orbit equivalence results to stable orbit equivalence

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.