We give a brief survey of some classification results on orbit equivalence of probability
measure preserving actions of countable groups. The notion of ℓ 2 Betti numbers for groups …

Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility,
and measures preserving group actions considered up to orbit equivalence. This title …

This volume provides a self-contained introduction to some topics in orbit equivalence
theory, a branch of ergodic theory. The first two chapters focus on hyperfiniteness and …

arXiv:1009.0132v1 [math.GR] 1 Sep 2010 Page 1 arXiv:1009.0132v1 [math.GR] 1 Sep 2010
Orbit Equivalence and Measured Group Theory Damien Gaboriau∗ May, 2010 Abstract We …

The title refers to the area of research which studies infinite groups using measure-theoretic
tools, and studies the restrictions that group structure imposes on ergodic theory of their …

Let G and H be infinite finitely generated amenable groups. This paper studies two notions
of equivalence between actions of such groups on standard Borel probability spaces. They …

A relative version of Connes' $\chi(M)$ invariant and existence of orbit inequivalent actions
Page 1 Ergod. Th. & Dynam. Sys. (2007), 27, 1199–1213 c 2007 Cambridge University Press …

We study the analogue, in orbit equivalence, of free product decompositions and free
indecomposability for countable groups. We introduce the (orbit equivalence invariant) …

Stability in orbit equivalence Page 1 Groups Geom. Dyn. 9 (2015), 203–235 DOI 10.4171/GGD/311
Groups, Geometry, and Dynamics ฉ European Mathematical Society Stability in orbit equivalence …

" The subject of this book is the study of ergodic, measure preserving actions of countable
discrete groups on standard probability spaces. It explores a direction that emphasizes a …