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St. Petersburg Seminar on Representation Theory and Dynamical Systems
February 24, 2021 17:00, St. Petersburg, Zoom, see http://www.pdmi.ras.ru/~rtheory/nextsem.html
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Cost of inner amenable equivalence relations
K. Wrobel Texas A&M University
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Abstract:
Cost is a $[1,\infty]$-valued measure-isomorphism invariant of aperiodic measured equivalence relations defined by Gilbert Levitt and heavily studied by Damien Gaboriau. For a large class of equivalence relations, including amenable, the cost is 1. Yoshikata Kida and Robin Tucker-Drob recently defined the notion of an inner amenable equivalence relation as an analog of inner amenability in the setting of groups. I will give an overview of the theory of cost and inner amenable groups as well as several previous related results. If time permits, I'll outline a proof that inner amenable equivalence relations also have cost 1. This is joint work with Robin Tucker-Drob.
Language: English
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