Relative Hyperbolicity, Trees of Spaces and Cannon-Thurston Maps
Group Theory
2011-03-24 v3 Geometric Topology
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.
Keywords
Cite
@article{arxiv.0708.3578,
title = {Relative Hyperbolicity, Trees of Spaces and Cannon-Thurston Maps},
author = {Mahan Mj and Abhijit Pal},
journal= {arXiv preprint arXiv:0708.3578},
year = {2011}
}
Comments
27pgs No figs, v3: final version, incorporating referee's comments, to appear in Geometriae Dedicata