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

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

 Loading the player... 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 Collection : Research talks ; Geometry ; Topology Format : MP4 (.mp4) - HD Durée : 00:57:01 Domaine : Topology ; Geometry 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-variétésOrganisateurs de la rencontre : Haïssinsky, Peter ; Paoluzzi, Luisa ; Walsh, GenevieveDates : 26/02/2018 - 02/03/2018 Année de la rencontre : 2018 URL Congrès : https://walsh-paoluzzi.weebly.com/conference.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

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