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- W2406069249 abstract "The purpose of this dissertation is to study some new notions of equivalenceof measure preserving group actions on probability spaces. Theseinclude approximate versions of conjugacy and orbit equivalence (OE) aswell as a notion of weak OE, which is engendered by the notion of weakconjugacy that was recently introduced by A. Kechris. We study the relationshipbetween our new notions and the classical ones. For instance,we show that approximate conjugacy is the same as conjugacy for actionsof groups with Kazhdan's property (T) whereas for groups with infiniteamenable quotients these notions are very much distinct. We also useresults of Monod-Shalom, Kida, and Chifan-Kida to deduce superrigidityresults within the paradigm of approximate conjugacy and OE. Moreover,we show that a number of invariants and properties are preserved by weakOE, including strong ergodicity. This allows us to deduce that any nonamenablegroup without Kazhdan's property (T) has at least two weaklyorbit inequivalent actions. This dissertation is largely based on the author'sjoint work with Professor Sorin Popa in the paper [AP15]." @default.
- W2406069249 created "2016-06-24" @default.
- W2406069249 creator A5039985959 @default.
- W2406069249 date "2016-01-01" @default.
- W2406069249 modified "2023-09-27" @default.
- W2406069249 title "Weak and approximate equivalence of group actions in the framework of ultrapower Cartan inclusions" @default.
- W2406069249 hasPublicationYear "2016" @default.
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