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arXiv · 1107.1357

Stable orbit equivalence of Bernoulli actions of free groups and isomorphism of some of their factor actions

Niels Meesschaert·Sven Raum·Stefaan Vaes
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Abstract

We give an elementary proof for Lewis Bowen's theorem saying that two Bernoulli actions of two free groups, each having arbitrary base probability spaces, are stably orbit equivalent. Our methods also show that for all compact groups K and every free product Γof n infinite amenable groups, the factor K^Γ/K of the Bernoulli action of Γon K^Γ by the diagonal action of K, is isomorphic with a Bernoulli action of Γ.

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Niels Meesschaert, Sven Raum, Stefaan Vaes. 2012-05-31. Stable orbit equivalence of Bernoulli actions of free groups and isomorphism of some of their factor actions. https://arxiv.org/abs/1107.1357

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