Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Dynamics, Geometry, & Groups Seminar


Friday, September 7th, 2018

Time: 10:30 a.m Place: Jeffery Hall 422

Speaker: Camille Horbez (Laboratoire de Mathématiques d’Orsay)

Title: Growth under automorphisms of hyperbolic groups

Abstract: Let G be a finitely generated group, let S be a finite generating set of G, and let f be an automorphism of G. A natural question is the following: what are the possible asymptotic behaviors for the length of f^n(g), written as a word in the generating set S, as n goes to infinity, and as g varies in the group G?

We investigate this question in the case where G is a torsion-free Gromov hyperbolic group. Growth was completely described by Thurston when G is the fundamental group of a hyperbolic surface, and can be understood from Bestvina-Handel’s work on train-tracks when G is a free group. We address the case of a general torsion-free hyperbolic group. We show in particular that every element g has a well-defined exponential growth rate under iteration of f, and that only finitely many exponential growth rates arise as g varies in G.

This is a joint work with Rémi Coulon, Arnaud Hilion and Gilbert Levitt.