Hyperbolic extensions of free groups from atoroidal ping-pong

Uyanik, Caglar

doi:10.2140/agt.2019.19.1385

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Hyperbolic extensions of free groups from atoroidal ping-pong

Caglar Uyanik

Algebraic & Geometric Topology 19 (2019) 1385–1411

DOI: 10.2140/agt.2019.19.1385

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 nonvirtually 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.

Keywords

free groups, hyperbolic extensions, $\mathrm{Out}(F_N)$, geodesic currents

Mathematical Subject Classification 2010

Primary: 20F28, 20F67

Secondary: 37D40

References

Publication

Received: 19 March 2018

Revised: 3 September 2018

Accepted: 3 October 2018

Published: 21 May 2019

Authors

Caglar Uyanik
Department of Mathematics Yale University New Haven, CT United States

Volume 19, issue 3 (2019)