Cannon–Thurston maps for hyperbolic free group extensions

@article{Dowdall2015CannonThurstonMF,
  title={Cannon–Thurston maps for hyperbolic free group extensions},
  author={Spencer Dowdall and Ilya Kapovich and Samuel J. Taylor},
  journal={Israel Journal of Mathematics},
  year={2015},
  volume={216},
  pages={753-797}
}
This paper gives a detailed analysis of the Cannon–Thurston maps associated to a general class of hyperbolic free group extensions. Let F denote a free group of finite rank at least 3 and consider a convex cocompact subgroup Γ ≤ Out(F), i.e. one for which the orbit map from Γ into the free factor complex of F is a quasi-isometric embedding. The subgroup Γ determines an extension EΓ of F, and the main theorem of Dowdall–Taylor [DT14] states that in this situation EΓ is hyperbolic if and only if… 
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