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Abstract
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We prove that all atoroidal automorphisms of
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
such that the corresponding free group extension is hyperbolic. Moreover, these
subgroups are not necessarily convex cocompact.
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Keywords
free groups, hyperbolic extensions, $\mathrm{Out}(F_N)$,
geodesic currents
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Mathematical Subject Classification 2010
Primary: 20F28, 20F67
Secondary: 37D40
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Publication
Received: 19 March 2018
Revised: 3 September 2018
Accepted: 3 October 2018
Published: 21 May 2019
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