Permanent link to this recordhttp://hdl.handle.net/20.500.12613/4822
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Abstract© 2018, Mathematical Sciences Publishers. All rights reserved. Given a finitely generated subgroup Γ≤Out(F) of the outer automorphism group of the rank-r free group F = Fr, there is a corresponding free group extension 1→F→EΓ→Γ→1. We give sufficient conditions for when the extension EΓ is hyperbolic. In particular, we show that if all infinite-order elements of Γ are atoroidal and the action of Γ on the free factor complex of F has a quasi-isometric orbit map, then EΓ is hyperbolic. As an application, we produce examples of hyperbolic F-extensions EΓ for which Γ has torsion and is not virtually cyclic. The proof of our main theorem involves a detailed study of quasigeodesics in Outer space that make progress in the free factor complex. This may be of independent interest.
Citation to related workMathematical Sciences Publishers
Has partGeometry and Topology
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