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H 1 Torsion groups do not act on 2-dimensional CAT(0) complexes

Auteurs : Przytycki, Piotr (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We show, under mild hypotheses, that if each element of a finitely generated group acting on a 2-dimensional CAT(0) complex has a fixed point, then the action is trivial. In particular, all actions of finitely generated torsion groups on such complexes are trivial. As an ingredient, we prove that the image of an immersed loop in a graph of girth 2π with length not commensurable to π has diameter > π. This is related to a theorem of Dehn on tiling rectangles by squares.
    This is joint work with Sergey Norin and Damian Osajda.

    Keywords : CAT(0) space; torsion group; rectangle tiling

    Codes MSC :
    20F65 - Geometric group theory

    Informations sur la rencontre

    Nom de la rencontre : Aspects of Non-Positive and Negative Curvature in Group Theory / Courbure négative et courbure négative ou nulle en théorie des groupes
    Organisateurs de la rencontre : Bromberg, Kenneth ; Hilion, Arnaud ; Kazachkov, Ilya ; Sageev, Michah ; Tao, Jing
    Dates : 17/06/2019 - 21/06/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/1958.html

    Citation Data

    DOI : 10.24350/CIRM.V.19539503
    Cite this video as: Przytycki, Piotr (2019). Torsion groups do not act on 2-dimensional CAT(0) complexes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19539503
    URI : http://dx.doi.org/10.24350/CIRM.V.19539503


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