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arXiv · 0708.3578

Relative Hyperbolicity, Trees of Spaces and Cannon-Thurston Maps

Mahan Mj·Abhijit Pal
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Abstract

We prove the existence of continuous boundary extensions (Cannon-Thurston maps) for the inclusion of a vertex space into a tree of (strongly) relatively hyperbolic spaces satisfying the qi-embedded condition. This implies the same result for inclusion of vertex (or edge) subgroups in finite graphs of (strongly) relatively hyperbolic groups. This generalises a result of Bowditch for punctured surfaces in 3 manifolds and a result of Mitra for trees of hyperbolic metric spaces.

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Mahan Mj, Abhijit Pal. 2007-08-27. Relative Hyperbolicity, Trees of Spaces and Cannon-Thurston Maps. https://doi.org/10.1007/s10711-010-9519-2

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