Twisting out fully irreducible automorphisms

TL;DR

This paper establishes an analogue of Thurston's theorem for the outer automorphism group of a free group, characterizing certain automorphisms as fully irreducible based on their generating Dehn twists.

Contribution

It extends Thurston's classification to free groups, identifying conditions under which automorphisms are fully irreducible.

Findings

Automorphisms generated by Dehn twists are fully irreducible unless conjugate to a power of a twist.

The theorem provides a criterion for fully irreducible automorphisms in free groups.

Analogue of Thurston's theorem for mapping class groups applied to free groups.

Abstract

By a theorem of Thurston, in the subgroup of the mapping class group generated by Dehn twists around two curves that fill, every element not conjugate to a power of one of the twist is pseudo-Anosov. We prove an analogue of this theorem for the outer automorphism group of a free group.