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Mathematics - Analysis | Topics in Orbit Equivalence

Topics in Orbit Equivalence

Series: Lecture Notes in Mathematics, Vol. 1852

Kechris, Alexander, Miller, Benjamin D.

2004, X, 138 p.

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  • About this book

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.

Content Level » Research

Keywords » Equivalence - amenability - cost - equivalence relations - hyperfiniteness - orbit equivalence - set - set theory

Related subjects » Analysis - Dynamical Systems & Differential Equations - Geometry & Topology - Mathematics

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