Subfactor projections

Abstract

When two free factors A and B of a free group F_n are in "general position" we define the projection of B to the splitting complex (alternatively, the complex of free factors) of A. We show that the projections satisfy properties analogous to subsurface projections introduced by Masur and Minsky. We use the subfactor projections to construct an action of Out(F_n) on a finite product of hyperbolic spaces where every automorphism with exponential growth acts with positive translation length. We also prove a version of the Bounded geodesic image theorem. In the appendix, we give a sketch of the proof of the Handel-Mosher hyperbolicity theorem for the splitting complex using (liberal) folding paths.

Appendix added in version 2

References in corpus (3)

• A note on subfactor projections
• Submanifold Projection
• Hyperbolicity of the Cyclic Splitting Complex

Cited by in corpus (12)

• Hierarchically hyperbolic spaces I: curve complexes for cubical groups
• Hyperbolic extensions of free groups
• Hyperbolic graphs for free products, and the Gromov boundary of the graph of cyclic splittings
• Relative free splitting and free factor complexes I: Hyperbolicity
• A note on subfactor projections
• Hyperbolic extensions of free groups from atoroidal ping-pong
• Automorphisms of graphs of cyclic splittings of free groups
• Fully irreducible Automorphisms of the Free Group via Dehn twisting in ${♯}_k(S^2\times S^1)$
• Convexity of balls in the outer space
• Limit sets of unfolding paths in Outer space
• Quasi-geodesics in Out(F_n) and their shadows in sub-factors
• Geometry of extensions of free groups via automorphisms with fixed points on the complex of free factors