On orbit equivalence of measure preserving actions
D. Gaboriau
Article publié :
Rigidity in dynamics and geometry (Cambridge, 2000), pages 167-186, Springer,
Berlin, 2002
Télécharger l'article : pdf
(270K), ps (190K), dvi
(80K)
Abstract
We give a brief survey of some classification results on orbit equivalence
of probability measure preserving countable group actions. The notion of
l2 Betti numbers for groups is gently introduced. An account
of orbit equivalence invariance for l2 Betti numbers is presented
together with a description of the theory of equivalence relation actions
on simplicial complexes. We relate orbit equivalence to a measure theoretic
analogue of commensurability and quasi-isometry of groups : measure equivalence.
Rather than a complete description of these subjects, a lot of examples
are provided.