Random outer automorphisms of free groups: Attracting trees and their singularity structures

Abstract

We prove that a "random" free group outer automorphism is an ageometric fully irreducible outer automorphism whose ideal Whitehead graph is a union of triangles. In particular, we show that its attracting (and repelling) tree is a nongeometric $\mathbb{R}$-tree all of whose branch points are trivalent

27 pages comments are welcome!