Topics in orbit equivalence
By: Alexander S. Kechris, Benjamin D. Miller.
Series: Lecture notes in mathematics ;; 1852; Lecture notes in mathematics (Springer-Verlag) ;; 1852.
Publisher: Springer
Published: 2004
Place of publication: Berlin; New York
Language: eng
Number of pages: 134
Subjects: Equivalence relations (Set theory); Ergodic theory; Topological transformation groups; Descriptive set theory
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.
Notes: Includes bibliographical references (p. 129-130) and index.
Also available online.