A note on subfactor projections

Abstract

We extend some results of [BF12] 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, i.e. 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.

13 pages

References in corpus (3)

• Subfactor projections
• Right-angled Artin groups and Out(F_n) I: quasi-isometric embeddings
• Submanifold Projection

Cited by in corpus (7)

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• Right-angled Artin groups and Out(F_n) I: quasi-isometric embeddings
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• Fully irreducible Automorphisms of the Free Group via Dehn twisting in ${♯}_k(S^2\times S^1)$
• Geometry of extensions of free groups via automorphisms with fixed points on the complex of free factors
• Limit sets of unfolding paths in Outer space