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Hyperbolic extensions of free groups from atoroidal ping-pong

Caglar Uyanik

Algebraic & Geometric Topology 19 (2019) 1385–1411

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

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free groups, hyperbolic extensions, $\mathrm{Out}(F_N)$, geodesic currents
Mathematical Subject Classification 2010
Primary: 20F28, 20F67
Secondary: 37D40
Received: 19 March 2018
Revised: 3 September 2018
Accepted: 3 October 2018
Published: 21 May 2019
Caglar Uyanik
Department of Mathematics
Yale University
New Haven, CT
United States