University of Arkansas Topology Seminar: 2/26/2015

Speaker: Caglar Uyanik

Title: Generalized north south dynamics on the space of geodesic currents

Abstract: The study of outer automorphism group of a free group Out(FN) is closely related to study of Mapping Class Groups. The Out(FN) analog of a pseudo-Anosov homeomorphism is called a fully irreducible or iwip (short for irreducible with irreducible powers). We will talk about types of iwips, geometric and hyperbolic, and prove that an iwip φ acts on the space of geodesic currents with some sort of north-south dynamics. As an application, we will give a criterion for subgroups of Out(FN) to contain a hyperbolic iwip.