Groups, Geometry, and Dynamics

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Volume 6, Issue 2, 2012, pp. 389–407
DOI: 10.4171/GGD/161

Published online: 2012-04-16

Universal Borel actions of countable groups

Simon Thomas[1]

(1) Rutgers University, Piscataway, United States

If the countable group $G$ has a nonabelian free subgroup, then there exists a standard Borel $G$-space such that the corresponding orbit equivalence relation is countable universal. In this paper, we will consider the question of whether the converse also holds.

Keywords: Borel equivalence relation, superrigidity, sofic groups

Thomas Simon: Universal Borel actions of countable groups. Groups Geom. Dyn. 6 (2012), 389-407. doi: 10.4171/GGD/161