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.
"Hyperbolic extensions of free groups from atoroidal ping-pong." Algebr. Geom. Topol. 19 (3) 1385 - 1411, 2019. https://doi.org/10.2140/agt.2019.19.1385