Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations.

Intro -- Contents -- Introduction -- Chapter 0. Preliminaries -- 0A. Actions -- 0B. Equivalence relations -- 0C. Borel notions -- 0D. Measures -- 0E. Borel actions and measures -- 0F. Amenability -- Chapter 1. Actions of Free Groups and Treeable Equivalence Relations -- Chapter 2. A Cocycle Reduction Result -- Chapter 3. Some Applications -- 3A. An "elementary" proof of existence of incomparables -- 3B. Further "elementary" proofs of theorems of Adams-Kechris -- 3C. "Elementary" proofs of results of Adams and Thomas -- 3D. Relative ergodicity and rigidity results for product group actions -- Chapter 4. Factoring Homomorphisms -- Chapter 5. Further Applications -- 5A. Rigidity results for reducibility and stable orbit equivalence -- 5B. Products of hyperbolic groups -- Chapter 6. Product Actions, I -- Chapter 7. Product Actions, II -- Chapter 8. A Final Application -- Appendix A: Strong Notions of Ergodicity -- A1. Homomorphisms and relative ergodicity -- A2. E[sub(0)]-ergodicity and almost invariant sets -- A3. Almost invariant vectors -- A4. E[sub(0)]-ergodicity of the shift action -- A5. Characterizations of amenable and Kazhdan groups -- A6. Mixing -- A7. Non-orbit equivalent relations -- Appendix B: Cocycles and Cocycle-invariant Functions -- B1. Review -- B2. α…invariant functions -- B3. α…invariant measures -- B4. Maximum two-supported measures -- Appendix C: Actions on Boundaries -- C1. Trees -- C2. Free groups -- C3. Free products of finite groups -- C4. Hyperbolic groups -- Appendix D: K-structured Equivalence Relations -- Appendix E: Proof of the General Case of Theorem 4.4 -- E1. Amenable classes of structures -- E2. The factoring lemma -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.