A note on subfactor projections

Abstract

We extend some results of Bestvina and Feighn [arXiv:1107.3308 (2011)] 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 $F_n$, ie, 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.