## Algebraic & Geometric Topology

### A note on subfactor projections

Samuel J Taylor

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 14, Number 2 (2014), 805-821.

Dates
Revised: 16 September 2013
Accepted: 16 September 2013
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715848

Digital Object Identifier
doi:10.2140/agt.2014.14.805

Mathematical Reviews number (MathSciNet)
MR3159971

Zentralblatt MATH identifier
1346.20057

Subjects
Secondary: 57M07: Topological methods in group theory

#### Citation

Taylor, Samuel J. A note on subfactor projections. Algebr. Geom. Topol. 14 (2014), no. 2, 805--821. doi:10.2140/agt.2014.14.805. https://projecteuclid.org/euclid.agt/1513715848

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