Volume 9, issue 4 (2009)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Quasi-convexity and shrinkwrapping

Hossein Namazi

Algebraic & Geometric Topology 9 (2009) 2443–2478
Abstract

We extend a result of Minsky to show that, for a map of a surface to a hyperbolic 3–manifold, which is 2–incompressible rel a geodesic link with a definite tube radius, the set of noncontractible simple loops with bounded length representatives is quasi-convex in the complex of curves of the surface. We also show how wide product regions can be used to find a geodesic link with a definite tube radius with respect to which a map is 2–incompressible.

Keywords
complex of curves, quasi-convexity, shrinkwrapping
Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 57N10, 30F40
References
Publication
Received: 12 January 2009
Revised: 27 September 2009
Accepted: 30 September 2009
Published: 22 November 2009
Authors
Hossein Namazi
Department of Mathematics
University of Texas at Austin
1 University Station C1200
Austin, TX 78712
http://ma.utexas.edu/users/hossein/