Quasi-convexity and shrinkwrapping

Namazi, Hossein

doi:10.2140/agt.2009.9.2443

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Quasi-convexity and shrinkwrapping

Hossein Namazi

Algebraic & Geometric Topology 9 (2009) 2443–2478

DOI: 10.2140/agt.2009.9.2443

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/

Volume 9, issue 4 (2009)