The automorphism group of Thompson's group F
Time and place
4 PM on Friday, March 19th, 2010; GC 5417
Jose Burillo (Universitat Politecnica de Catalunya)
Abstract
After work by Matt Brin, we know that the automorphism group of $F$ can be represented by conjugation by a piecewise linear map on the real line. We can use this fact to deduce many properties of the group of automorphisms. Brin found already a short exact sequence which defines the group in terms of $F$ and Thompson's group $T$, and shows it is finitely presented. To aid in understanding the group of automorphisms of $F$ we will introduce infinite periodic binary trees, which capture automorphisms of $F$ the same way that finite trees capture elements of $F$. We will show a presentation for Aut $F$ and study some interesting subgroups. Namely, the structure of Aut $F$ suggests some actions of $F$ on itself which have nice geometric interpretations, yielding subgroups isomorphic to $F\rtimes F$. Presentations for these subgroups will also be shown.
This is joint work with Sean Cleary.
