Algebraic & Geometric Topology

A note on subfactor projections

Samuel J Taylor

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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

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

Received: 15 August 2013
Revised: 16 September 2013
Accepted: 16 September 2013
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 57M07: Topological methods in group theory

subfactor projections $\operatorname{Out}(F_n)$ fully irreducible automorphisms


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

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