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H 2 Automorphisms of hyperbolic groups and growth

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

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automorphism and growth surface group free groups hyperbolic groups limiting tree dynamical setting and drift Karlsson-Ledrappier argument questions from the audience

Résumé : Let $G$ be a torsion-free hyperbolic group, let $S$ be a finite generating set of $G$, and let $f$ be an automorphism of $G$. We want to understand the possible growth types for the word length of $f^n(g)$, where $g$ is an element of $G$. Growth was completely described by Thurston when $G$ is the fundamental group of a hyperbolic surface, and can be understood from Bestvina-Handel's work on train-tracks when $G$ is a free group. We address the general case of a torsion-free hyperbolic group $G$; we show that every element in $G$ has a well-defined exponential growth rate under iteration of $f$, and that only finitely many exponential growth rates arise as $g$ varies in $G$. In addition, we show the following dichotomy: every element of $G$ grows either exponentially fast or polynomially fast under iteration of $f$.
This is a joint work with Rémi Coulon, Arnaud Hilion and Gilbert Levitt.

Codes MSC :
20E06 - Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20E36 - Automorphisms of infinite groups
20F34 - Fundamental groups and their automorphisms
20F65 - Geometric group theory
20F67 - Hyperbolic groups and nonpositively curved groups
57M07 - Topological methods in group theory

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 01/03/2018
    Date de captation : 20/02/2018
    Collection : Research talks ; Geometry ; Topology
    Format : MP4 (.mp4) - HD
    Durée : 01:10:24
    Domaine : Geometry ; Topology
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2018-02-20_Horbez.mp4

Informations sur la rencontre

Nom de la rencontre : Geometry of groups and 3-manifolds: state of the art and perspectives / Géométrie des groupes et géométrie des 3-variétés : situation et perspectives
Organisateurs de la rencontre : Bowditch, Brian H. ; Haïssinsky, Peter ; Los, Jérôme ; Short, Hamish
Dates : 19/02/2018 - 23/02/2018
Année de la rencontre : 2018
URL Congrès : https://conferences.cirm-math.fr/1894.html

Citation Data

DOI : 10.24350/CIRM.V.19361403
Cite this video as: Horbez, Camille (2018). Automorphisms of hyperbolic groups and growth. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19361403
URI : http://dx.doi.org/10.24350/CIRM.V.19361403

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