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Robin Tucker-Drob - Amenable subrelations of treed equivalence relations and the Paddle-ball lemma

Ort: Paulinum P-801

We give a comprehensive structural analysis of amenable subrelations of a treed measure-class-preserving equivalence relation. The main philosophy is to understand the behavior of the Radon-Nikodym cocycle in terms of the geometry of the amenable subrelation within the treeing. This allows us to extend structural results that were previously only known in the measure-preserving setting, e.g., we show that every nowhere smooth amenable subrelation is contained in a unique maximal amenable subrelation. Two of the main ingredients are an extension of Carrière and Ghys's criterion for nonamenability, along with a new Ping-Pong-style argument we call the "Paddle-ball lemma" that we use to apply this criterion in our setting. This is joint work with Anush Tserunyan.

Seminar webpage: https://www.math.uni-leipzig.de/~grabowski/acseminar/">https://www.math.uni-leipzig.de/~grabowski/acseminar/

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Beginn: June 1, 2023, 1:15 p.m.

Ende: June 1, 2023, 2:15 p.m.