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arXiv · 1205.5123

Stability in orbit equivalence for Baumslag-Solitar groups and Vaes groups

Yoshikata Kida
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Abstract

A measure-preserving action of a discrete countable group on a standard probability space is called stable if the associated equivalence relation is isomorphic to its direct product with the ergodic hyperfinite equivalence relation of type II_1. We show that any Baumslag-Solitar group has such an ergodic, free and stable action. It follows that any Baumslag-Solitar group is measure equivalent to its direct product with any amenable group. The same property is obtained for the inner amenable groups of Vaes.

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Yoshikata Kida. 2012-05-23. Stability in orbit equivalence for Baumslag-Solitar groups and Vaes groups. https://doi.org/10.4171/ggd%2F311

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