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Topics in Orbit Equivalence

  • Book
  • © 2004

Overview

Authors:
  1. Alexander S. Kechris
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1852)

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Table of contents (5 chapters)

  1. Front Matter

    Pages N2-X
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  2. I. Orbit Equivalence

    • Alexander S. Kechris, Benjamin D. Miller
    Pages 1-6

  3. II. Amenability and Hyperfiniteness

    • Alexander S. Kechris, Benjamin D. Miller
    Pages 7-53

  4. III. Costs of Equivalence Relations and Groups

    • Alexander S. Kechris, Benjamin D. Miller
    Pages 55-128

  5. References

    • Alexander S. Kechris, Benjamin D. Miller
    Pages 129-130

  6. Index

    • Alexander S. Kechris, Benjamin D. Miller
    Pages 131-134

  7. Back Matter

    Pages 129-135
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Keywords

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.

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