Algebra/Topology Seminar by Kaidi Ye

Algebra/Topology seminar by Kaidi Ye (Toronto)

Title: Geometric outer automrphisms of Fn

Abstract: I'll present in this talk some recent results about geometric outer automorphisms of free groups. Given S a compact surface and h: S --> S a homeomorphism on S, h induces naturally an outer automorphism on the fundamental group. We are interested in the "inverse" of this question: 

    Given an outer automorphism \phi on a group G, when is \phi induced by a homeomorphism on a surface ?  

It's shown in a Theorem of Dehn-Nielsen-Baer that, if G is isomorphic to the fundamental group of a closed compact surface, then every outer automorphism on G is geometric. However this theorem doesn't apply to the case where G is a free group. The main result that I want to present in this talk is an algorithm which decides whether a polynomially growing outer automorphism \phi of Fn admits a power which is geometric.