A note on subfactor projections

TL;DR

This paper extends results on subfactor projections in free groups, establishing well-defined projections with bounded diameter and applying these to construct fully irreducible automorphisms using a Bounded Geodesic Image Theorem.

Contribution

It generalizes subfactor projection properties and introduces a method to construct fully irreducible outer automorphisms in free groups.

Findings

Projections are well-defined with uniformly bounded diameter unless specific conditions hold.

Projections satisfy properties analogous to subsurface projections.

Application of the Bounded Geodesic Image Theorem to automorphism construction.

Abstract

We extend some results of [BF12] on subfactor projections to show that the projection of a free factor B to the free factor complex of the free factor A is well-defined with uniformly bound diameter, unless either A is contained in B or A and B are vertex stabilizers of a single splitting of F_n, i.e. they are disjoint. These projections are shown to satisfy properties analogous to subsurface projections, and we give as an application a construction of fully irreducible outer automorphisms using the Bounded Geodesic Image Theorem.