Tuesday, November 15, 2016 - 3:30pm to 4:30pm
- 4607B South Hall
Title: Hyperbolicity in Outer space with applications to free group extensions
Abstract: The "Outer space" of the rank n free group F_n is a contractible metric space on which the Outer automorphism group Out(F_n) acts properly discontinuously
. It was introduced by Culler and Vogtmann in 1986 and is now an important tool for the topological and geometric study of Out(F_n).
This talk will focus on the geometry of Outer space and implications for free group extensions. The first aspects of hyperbolicity in Outer space were discovered by Algom-Kfir, who showed that axes of fully irreducible automorphisms are strongly contracting. In this talk I will present a characterizatio
n of this strongly contracting property in terms of the geodesic's projection to the free factor complex. This characterizatio n allows one to exploit the hyperbolicity of Outer space to study many geometric aspects of free group extensions. Results here include a flexible means of producing hyperbolic free group extensions, qualitative statements regarding their structure and quasiconvex subgroups, and quantitative results about their Cannon-Thurston maps. Mostly joint with Sam Taylor, and some joint with Ilya Kapovich and Sam Taylor.
August 30, 2019 - 2:44pm