Hyperbolic extensions of free groups from atoroidal ping-pong

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Hyperbolic extensions of free groups

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 o...

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ژورنال

عنوان ژورنال: Algebraic & Geometric Topology

سال: 2019

ISSN: 1472-2739,1472-2747

DOI: 10.2140/agt.2019.19.1385