# 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…

## 13 Citations

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Let $G$ be a non-elementary word-hyperbolic group acting as a convergence group on a compact metrizable space $Z$ so that there exists a continuous $G$-equivariant map $i:\partial G\to Z$, which we…

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