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Full groups, cost, symmetric groups and IRSS

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Authors : Le Maître, François (Author of the conference)
CIRM (Publisher )

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Abstract : In this talk, we will first review some of the analogies between full groups of measure-preserving equivalence relations and the symmetric group over the integers, which have been used by A. Eisenmann and Y. Glasner to provide interesting examples of invariant random subgroups (IRSs) of the free group.
We will then see how the notion of cost, introduced by G. Levitt, naturally enters this picture. After that, we will explain how a stronger analogy between full groups and the symmetric group over the integers holds in the type III case.
A joint result with A. Kaïchouh which uses this analogy will be presented : full groups of hyperfinite type III equivalence relations have ample generics. This provides a positive answer to a question of A. Kechris and C. Rosendal on the existence of connected Polish group with ample generics.

MSC Codes :
37A05 - Measure-preserving transformations

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 30/07/15
    Conference Date : 14/07/15
    Subseries : Research talks
    arXiv category : Group Theory ; Dynamical Systems
    Mathematical Area(s) : Algebraic & Complex Geometry ; Algebra
    Format : MP4 (.mp4) - HD
    Video Time : 1:02:16
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2015-07-14_Le_Maitre.mp4

Information on the Event

Event Title : Impact of geometric group theory / Impacts de la géométrie des groupes
Event Organizers : Arzhantseva, Goulnara N. ; Bedaride, Nicolas ; Gaboriau, Damien ; Hilion, Arnaud
Dates : 13/07/15 - 17/07/15
Event Year : 2015
Event URL : http://conferences.cirm-math.fr/1224.html

Citation Data

DOI : 10.24350/CIRM.V.18798403
Cite this video as: Le Maître, François (2015). Full groups, cost, symmetric groups and IRSS. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18798403
URI : http://dx.doi.org/10.24350/CIRM.V.18798403

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