Hyperbolic extensions of free groups from atoroidal ping-pong

Abstract

We prove that all atoroidal automorphisms of $Out(F_N)$ act on the space of projectivized geodesic currents with generalized north-south dynamics. As an application, we produce new examples of non virtually cyclic, free and purely atoroidal subgroups of $Out(F_N)$ such that the corresponding free group extension is hyperbolic. Moreover, these subgroups are not necessarily convex cocompact.

v3: 17pp, 1 figure, minor corrections and clarifications following the referee's comments

References in corpus (3)

• The co-surface graph and the geometry of hyperbolic free group extensions
• Simultaneous construction of hyperbolic isometries
• Perron-Frobenius theory and frequency convergence for reducible substitutions

Cited by in corpus (3)

• Regluing graphs of Free Groups
• Atoroidal dynamics of subgroups of Out(F_N)
• Limit pretrees for free group automorphisms: existence