Short geodesics in hyperbolic 3-manifolds

Details Short geodesics in hyperbolic 3-manifolds Short geodesics in hyperbolic 3-manifolds

2009-12-17

arxiv.org/abs/0912.3496v2

Mathematics

Geometric Topology

12 pages, corrected Lemma 1

Scientific paper

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 $S$.

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