Topology Seminar: Fully irreducible outer automorphisms of a free group

Abstract: Fully irreducible outer automorphisms of a free group are analogous to loxodromic isometries of hyperbolic space, or to pseudo-Anosov elements of the mapping class group of a surface. We develop methods for constructing customized fully irreducible elements of a free group F of rank k. For example, there exists for any matrix A in GL(k,Z) a non-geometric fully irreducible element inducing the action of A on the non-abelian free group of rank k. This is an analogue of a well-known theorem for the mapping class group. This is joint work with Matt Clay.