The Tits Alternative for $Out(F_n)$ II: A Kolchin Type Theorem

TL;DR

This paper completes the proof of the Tits alternative for Out(F_n) by establishing a Kolchin type theorem that characterizes unipotent automorphisms as conjugate to upper-triangular subgroups.

Contribution

It introduces a Kolchin type theorem for Out(F_n), showing unipotent automorphisms can be conjugated into upper-triangular form, advancing the understanding of subgroup structure.

Findings

Finitely generated unipotent subgroups are conjugate to upper-triangular groups.

The proof completes the Tits alternative for Out(F_n).

The approach uses train-track representations.

Abstract

The proof of the Tits alternative for $Out(F_n)$ is completed. The main tool is a Kolchin type theorem, proved in this paper. It states that a finitely generated subgroup of $Out(F_n)$ consisting of unipotent automorphisms can be conjugated into an upper-triangular subgroup (this is interpreted via train-tracks).