The visual boundary of hyperbolic free-by-cyclic groups | Vidéo | Carmin.tv

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Chapters

The visual boundary of hyperbolic free-by-cyclic groups

Appears in collection : Jean-Morlet chair: Structure of 3-manifold groups / Chaire Jean-Morlet : Structures des groupes de 3-variétés

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.

Information about the video

Date of recording 27/02/2018
Date of publication 07/03/2018
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19368603
Cite this video Stark, Emily (27/02/2018). The visual boundary of hyperbolic free-by-cyclic groups. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19368603
URL https://dx.doi.org/10.24350/CIRM.V.19368603

Domain(s)

Bibliography

Algom-Kfir, Y., Hilion, A., & Stark, E. (2018). The visual boundary of hyperbolic free-by-cyclic groups. <arXiv:1801.04750> - https://arxiv.org/abs/1801.04750

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