A note on subfactor projections

Abstract

We extend some results of Bestvina and Feighn [4] 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 Fn, 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.