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The visual boundary of hyperbolic free-by-cyclic groups
Post-edited
Authors : Stark, Emily (Author of the conference)
CIRM (Publisher )
20E36 - Automorphisms of infinite groups
20F65 - Geometric group theory
20F67 - Hyperbolic groups and nonpositively curved groups
CIRM (Publisher )
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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 |
Abstract :
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.
MSC Codes : 20E36 - Automorphisms of infinite groups
20F65 - Geometric group theory
20F67 - Hyperbolic groups and nonpositively curved groups
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 07/03/2018 Conference Date : 27/02/2018 Subseries : Research talks arXiv category : Geometric Topology ; Group Theory Mathematical Area(s) : Topology ; Geometry Format : MP4 (.mp4) - HD Video Time : 00:57:01 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-02-27_Stark.mp4 
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Information on the Event
Event Title : Jean-Morlet chair: Structure of 3-manifold groups / Chaire Jean-Morlet : Structures des groupes de 3-variétésEvent Organizers : Haïssinsky, Peter ; Paoluzzi, Luisa ; Walsh, Genevieve Dates : 26/02/2018 - 02/03/2018 Event Year : 2018 Event URL : https://www.chairejeanmorlet.com/1904.html
Citation Data
DOI : 10.24350/CIRM.V.19368603Cite 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 |
Bibliography
- Algom-Kfir, Y., Hilion, A., & Stark, E. (2018). The visual boundary of hyperbolic free-by-cyclic groups.
