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

Primary: 57M50

Secondary: 30F40, 57N10

References

Publication

Received: 12 January 2009
Revised: 27 September 2009
Accepted: 30 September 2009
Published: 22 November 2009

Authors