A Bers-like proof of the existence of train tracks for free group automorphisms

TL;DR

This paper provides a new proof of the train track theorem for free group automorphisms using Lipschitz distance on Outer space, offering an alternative approach to a fundamental result in geometric group theory.

Contribution

It introduces a Bers-like proof technique leveraging Lipschitz metrics, differing from traditional combinatorial methods.

Findings

Validates the existence of train tracks via Lipschitz distance

Offers an alternative proof method for the train track theorem

Enhances understanding of automorphisms of free groups

Abstract

Using Lipschitz distance on Outer space we give another proof of the train track theorem.