Topics in Orbit Equivalence
Published on 8. September 2004
X, 138 pages
978-3-540-44508-1 (ISBN)
Description
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.
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Alexander Kechris | Benjamin D. Miller
Topics in Orbit Equivalence
Book
08/2004
Springer
€40.65
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Content
Preface.- I. Orbit Equivalence.- II. Amenability and Hyperfiniteness.- III. Costs of Equivalence Relations and Groups.- References.- Index.
