Groups, Geometry, and Dynamics


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Volume 5, Issue 1, 2011, pp. 17–38
DOI: 10.4171/GGD/115

Published online: 2011-01-19

Stable orbit equivalence of Bernoulli shifts over free groups

Lewis Bowen[1]

(1) The University of Texas at Austin, USA

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.

Keywords: Stable orbit equivalence, Bernoulli shifts, free groups

Bowen Lewis: Stable orbit equivalence of Bernoulli shifts over free groups. Groups Geom. Dyn. 5 (2011), 17-38. doi: 10.4171/GGD/115