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H 1 Measure equivalence and right-angled Artin groups

Auteurs : Horbez, Camille (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Given a finite simple graph X, the right-angled Artin group associated to X is defined by the following very simple presentation: it has one generator per vertex of X, and the only relations consist in imposing that two generators corresponding to adjacent vertices commute. We investigate right-angled Artin groups from the point of view of measured group theory. Our main theorem is that two right-angled Artin groups with finite outer automorphism groups are measure equivalent if and only if they are isomorphic. On the other hand, right-angled Artin groups are never superrigid from this point of view: given any right-angled Artin group G, I will also describe two ways of producing groups that are measure equivalent to G but not commensurable to G.This is joint work with Jingyin Huang.

    Keywords : right-angled Artin groups; measure equivalence; orbit equivalence; rigidity

    Codes MSC :
    20F36 - Braid groups; Artin groups
    20F65 - Geometric group theory
    37A20 - Orbit equivalence, cocycles, ergodic equivalence relations

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 23/10/2020
      Date de captation : 08/10/2020
      Collection : Research talks ; Geometry
      Format : MP4
      Durée : 00:49:33
      Domaine : Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2020-10-08_Horbez.mp4

    Informations sur la rencontre

    Nom de la rencontre : Measured and Geometric Group Theory, Rigidity, Operator Algebras / Théorie mesurée et géométrique des groupes, rigidité, algèbres d’opérateurs
    Organisateurs de la rencontre : Gaboriau, Damien ; Houdayer, Cyril ; Szöke, Nóra Gabriella ; Tessera, Romain
    Dates : 05/10/2020 - 10/10/2020
    Année de la rencontre : 2020
    URL Congrès : https://conferences.cirm-math.fr/2435.html

    Citation Data

    DOI : 10.24350/CIRM.V.19657603
    Cite this video as: Horbez, Camille (2020). Measure equivalence and right-angled Artin groups. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19657603
    URI : http://dx.doi.org/10.24350/CIRM.V.19657603


    Voir aussi

    Bibliographie

    1. HORBEZ, Camille et HUANG, Jingyin. Measure equivalence classification of transvection-free right-angled Artin groups. arXiv preprint arXiv:2010.03613, 2020. - https://arxiv.org/abs/2010.03613

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