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H 2 The visual boundary of hyperbolic free-by-cyclic groups

Auteurs : Stark, Emily (Auteur de la Conférence)
CIRM (Editeur )

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free-by-cyclic groups Menger curve theorem mapping tori visual boundary Cannon-Thurston map structure of the Cannon-Thurston map $\mathcal{Q}$-map band complex

Résumé : Given an automorphism of the free group, we consider the mapping torus defined with respect to the automorphism. If the automorphism is atoroidal, then the resulting free-by-cyclic group is hyperbolic by work of Brinkmann. In addition, if the automorphism is fully irreducible, then work of Kapovich-Kleiner proves the boundary of the group is homeomorphic to the Menger curve. However, their proof is very general and gives no tools to further study the boundary and large-scale geometry of these groups. In this talk, I will explain how to construct explicit embeddings of non-planar graphs into the boundary of these groups whenever the group is hyperbolic. Along the way, I will illustrate how our methods distinguish free-by-cyclic groups which are the fundamental group of a 3-manifold. This is joint work with Yael Algom-Kfir and Arnaud Hilion.

Codes MSC :
20E36 - Automorphisms of infinite groups
20F65 - Geometric group theory
20F67 - Hyperbolic groups and nonpositively curved groups

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 07/03/2018
    Date de captation : 27/02/2018
    Sous collection : Research talks
    arXiv category : Geometric Topology ; Group Theory
    Domaine : Topology ; Geometry
    Format : MP4 (.mp4) - HD
    Durée : 00:57:01
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2018-02-27_Stark.mp4

Informations sur la rencontre

Nom de la rencontre : Jean-Morlet chair: Structure of 3-manifold groups / Chaire Jean-Morlet : Structures des groupes de 3-variétés
Organisateurs de la rencontre : Haïssinsky, Peter ; Paoluzzi, Luisa ; Walsh, Genevieve
Dates : 26/02/2018 - 02/03/2018
Année de la rencontre : 2018
URL Congrès : https://www.chairejeanmorlet.com/1904.html

Citation Data

DOI : 10.24350/CIRM.V.19368603
Cite this video as: Stark, Emily (2018). The visual boundary of hyperbolic free-by-cyclic groups. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19368603
URI : http://dx.doi.org/10.24350/CIRM.V.19368603