Volume 11, issue 2 (2011)

 Recent Issues
Author Index
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 To Appear Other MSP Journals
Short geodesics in hyperbolic $3$–manifolds

William Breslin

Algebraic & Geometric Topology 11 (2011) 735–745
Abstract

For each $g\ge 2$, we prove existence of a computable constant $ϵ\left(g\right)>0$ such that if $S$ is a strongly irreducible Heegaard surface of genus $g$ in a complete hyperbolic $3$–manifold $M$ and $\gamma$ is a simple geodesic of length less than $ϵ\left(g\right)$ in $M$, then $\gamma$ is isotopic into $S$.

Keywords
Heegaard surface, hyperbolic $3$–manifold, geodesic
Primary: 57M50