Topics in Orbit Equivalence

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August 2004



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 amenability. Included here are proofs of Dye's theorem that probability measure-preserving, ergodic actions of the integers are orbit equivalent and of the theorem of Connes-Feldman-Weiss identifying amenability and hyperfiniteness for non-singular equivalence relations. The presentation here is often influenced by descriptive set theory, and Borel and generic analogs of various results are discussed. The final chapter is a detailed account of Gaboriau's recent results on the theory of costs for equivalence relations and groups and its applications to proving rigidity theorems for actions of free groups.


Preface. - I. Orbit Equivalence. - II. Amenability and Hyperfiniteness. - III. Costs of Equivalence Relations and Groups. - References. - Index.


EAN: 9783540226031
ISBN: 3540226036
Untertitel: 'Lecture Notes in Mathematics'. 2004. Auflage. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: August 2004
Seitenanzahl: 148 Seiten
Format: kartoniert
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