Topics in Orbit Equivalence

2004
ISBN: 978-3-540-22603-1
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1852, 138 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 236 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Miller, Benjamin D.

Kechris, Alexander

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

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