Cannon–Thurston maps for pared manifolds of bounded geometry

Mj, Mahan

doi:10.2140/gt.2009.13.189

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Cannon–Thurston maps for pared manifolds of bounded geometry

Mahan Mj

Geometry & Topology 13 (2009) 189–245

DOI: 10.2140/gt.2009.13.189

Abstract

Let $N^{h} \in H (M, P)$ 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

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/

Volume 13, issue 1 (2009)