Relative hyperbolicity, trees of spaces and Cannon-Thurston maps

Mahan, Mj. ; Abhijit, Pal (2011) Relative hyperbolicity, trees of spaces and Cannon-Thurston maps Geometriae Dedicata, 151 (1). pp. 59-78. ISSN 0046-5755

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Official URL: http://www.springerlink.com/index/42T513479U57507G...

Related URL: http://dx.doi.org/10.1007/s10711-010-9519-2

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 generalizes a result of Bowditch for punctured surfaces in 3 manifolds and a result of Mitra for trees of hyperbolic metric spaces.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Relative Hyperbolicity; Cannon-Thurston Maps; Trees of Spaces
ID Code:89538
Deposited On:28 Apr 2012 12:57
Last Modified:19 May 2016 04:04

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