Short geodesics in hyperbolic 3-manifolds

Abstract

For each $g\ge 2$, we prove existence of a computable constant $\epsilon (g)>0$ 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 $\epsilon (g)$ in $M$, then $\gamma$ is isotopic into $S$.

12 pages, corrected Lemma 1

References in corpus (1)

• Locally unknotted spines of Heegaard splittings

Cited by in corpus (3)

• Explicit Dehn filling and Heegaard splittings
• Complex length of short curves and Minimal Fibration in hyperbolic $3$-Manifolds fibering over the circle
• Uniform models and short curves for random 3-manifolds