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Hyperbolic extensions of free groups from atoroidal ping-pong (1711.07923v3)

Published 21 Nov 2017 in math.GR and math.GT

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.

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