On Orbit Equivalence of Measure Preserving Actions

Damien Gaboriau ()
Additional contact information
Damien Gaboriau: Unité de Mathématiques Pures et Appliquées, UMR CNRS 5669

A chapter in Rigidity in Dynamics and Geometry, 2002, pp 167-186 from Springer

Abstract: Abstract We give a brief survey of some classification results on orbit equivalence of probability measure preserving actions of countable groups. 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.

Keywords: Equivalence Relation; Simplicial Complex; Cayley Graph; Betti Number; Fundamental Domain (search for similar items in EconPapers)
Date: 2002
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04743-9_8

Ordering information: This item can be ordered from
http://www.springer.com/9783662047439

DOI: 10.1007/978-3-662-04743-9_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().