Stability in Outer Space

2014/11/09 by Hamenstädt, Ursula, Hensel, Sebastian
#20F34 #20F65 #57M07 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1411.2281

Abstract

We characterize strongly Morse quasi-geodesics in Outer space as quasi-geodesics which project to quasi-geodesics in the free factor graph. We define convex cocompact subgroups of Out(F_n) as subgroups such that an orbit map in the free factor graph is a quasi-isometric embedding, and we characterize such groups via their action on Outer space in a way which resembles the characterization of convex cocompact subgroups of mapping class groups.

Related

• Contracting orbits in Outer space
• The local-to-global property for Morse quasi-geodesics
• Morse properties in convex projective geometry
• Quasi-convexity of hyperbolically embedded subgroups
• Regularity of Morse geodesics and growth of stable subgroups