University of Arkansas Topology Seminar: 4/30/2015

Speaker: Spencer Dowdall

Title:Hyperbolic free group extensions and contracting orbits in Outer space

Abstract: Every subgroup G of the outer automorphism group of a finite-rank free group F naturally determines a free group extension 1 → F → EGG → 1. In this talk, I will discuss geometric conditions on the subgroup G that imply the corresponding extension EG is hyperbolic. Our conditions are in terms of the free factor complex and are related to certain aspects of hyperbolicity in the Culler−Vogtmann Outer space of F. As an application, we construct new examples of hyperbolic free group extensions. Joint with Samuel Taylor.