#### Volume 13, issue 1 (2009)

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Cannon–Thurston maps for pared manifolds of bounded geometry

### Mahan Mj

Geometry & Topology 13 (2009) 189–245
##### Abstract

Let ${N}^{h}\in H\left(M,P\right)$ be a hyperbolic structure of bounded geometry on a pared manifold such that each component of ${\partial }_{0}M=\partial M-P$ is incompressible. We show that the limit set of ${N}^{h}$ is locally connected by constructing a natural Cannon–Thurston map. This provides a unified treatment, an alternate proof and a generalization of results due to Cannon and Thurston, Minsky, Bowditch, Klarreich and the author.

##### Keywords
Cannon–Thurston Maps, local connectivity of limit sets
Primary: 57M50