Cannon–Thurston maps for pared manifolds of bounded geometry

Mj, Mahan¹

¹ School of Mathematical Sciences, RKM Vivekananda University, PO Belur Math, Dt Howrah, WB-711202, India

Geometry & topology, Tome 13 (2009) no. 1, pp. 189-245.

Résumé

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.

Détail

DOI : 10.2140/gt.2009.13.189

Keywords: Cannon–Thurston Maps, local connectivity of limit sets

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