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 , are nonabelian free groups of finite rank then every nontrivial Bernoulli shift over is stably orbit equivalent to every nontrivial Bernoulli shift over . This answers a question of S. Popa.
Cite this article
Lewis Bowen, Stable orbit equivalence of Bernoulli shifts over free groups. Groups Geom. Dyn. 5 (2011), no. 1, pp. 17–38DOI 10.4171/GGD/115