Relative Hyperbolicity, Trees of Spaces and Cannon-Thurston Maps

Details Relative Hyperbolicity, Trees of Spaces and Cannon-Thurston Maps Relative Hyperbolicity, Trees of Spaces and Cannon-Thurston Maps

2007-08-27

arxiv.org/abs/0708.3578v3

Geometriae Dedicata, 2011, Volume 151, Number 1, 59-78

Mathematics

Group Theory

27pgs No figs, v3: final version, incorporating referee's comments, to appear in Geometriae Dedicata

Scientific paper

10.1007/s10711-010-9519-2

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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