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 Nh H(M,P) be a hyperbolic structure of bounded geometry on a pared manifold such that each component of 0M = M P is incompressible. We show that the limit set of Nh 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
Mathematical Subject Classification 2000
Primary: 57M50
References
Publication
Received: 17 February 2006
Revised: 18 September 2008
Accepted: 17 September 2008
Preview posted: 3 November 2008
Published: 1 January 2009
Proposed: Jean-Pierre Otal
Seconded: Benson Farb, Dave Gabai
Authors
Mahan Mj
School of Mathematical Sciences
RKM Vivekananda University
PO Belur Math
Dt Howrah
WB-711202
India
http://people.rkmvu.ac.in/~mahan/