Cannon-Thurston Maps for Pared Manifolds of Bounded Geometry

Details Cannon-Thurston Maps for Pared Manifolds of Bounded Geometry Cannon-Thurston Maps for Pared Manifolds of Bounded Geometry

2005-03-25

arxiv.org/abs/math/0503581v6

Geom. Topol. 13 (2009), no. 1, 189-245

Mathematics

Geometric Topology

57 pages, 4 figures, Final version incorporating referee's comments. To appear in Geometry and Topology

Scientific paper

10.2140/gt.2009.13.189

Let N^h be a hyperbolic 3-manifold of bounded geometry corresponding to a hyperbolic structure on a pared manifold (M,P). Further, suppose that (\partial{M} - P) is incompressible, i.e. the boundary of M is incompressible away from cusps. Further, suppose that M_{gf} is a geometrically finite hyperbolic structure on (M,P). Then there is a Cannon- Thurston map from the limit set of M_{gf} to that of N^h. Further, the limit set of N^h is locally connected. This answers in part a question attributed to Thurston.

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