#### Volume 9, issue 4 (2009)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear 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