Volume 14, issue 2 (2014)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 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.

Keywords
subfactor projections, $\operatorname{Out}(F_n)$, fully irreducible automorphisms
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 57M07
References
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/