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H 1 Full groups, cost, symmetric groups and IRSS

Auteurs : Le Maître, François (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : 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.

    Codes MSC :
    37A05 - Measure-preserving transformations

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 30/07/15
      Date de captation : 14/07/15
      Collection : Research Talks ; Algebra ; Algebraic and Complex Geometry
      Format : quicktime ; audio/x-aac
      Durée : 1:02:16
      Domaine : Algebraic & Complex Geometry ; Algebra
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-07-14_Le_Maitre.mp4

    Informations sur la rencontre

    Nom de la rencontre : Impact of geometric group theory / Impacts de la géométrie des groupes
    Organisateurs de la rencontre : Arzhantseva, Goulnara N. ; Bedaride, Nicolas ; Gaboriau, Damien ; Hilion, Arnaud
    Dates : 13/07/15 - 17/07/15
    Année de la rencontre : 2015
    URL Congrès : 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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