publiée le 3 mai 2024
Laminations and structure theorems for group actions on the line - Part 1
De Michele Triestino
The visual boundary of hyperbolic free-by-cyclic groups
De Emily Stark
Apparaît dans la 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.
