#### Volume 14, issue 2 (2014)

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A note on subfactor projections

### Samuel J Taylor

Algebraic & Geometric Topology 14 (2014) 805–821
##### 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.

##### Keywords
subfactor projections, $\operatorname{Out}(F_n)$, fully irreducible automorphisms
Primary: 20F65
Secondary: 57M07
##### Publication
Received: 15 August 2013
Revised: 16 September 2013
Accepted: 16 September 2013
Published: 30 January 2014
##### Authors
 Samuel J Taylor Department of Mathematics University of Texas at Austin 1 University Station C1200 Austin, TX 78712 USA http://www.ma.utexas.edu/users/staylor/