Short geodesics in hyperbolic 3–manifolds

William Breslin
2011 Algebraic and Geometric Topology  
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 $S$.
doi:10.2140/agt.2011.11.735 fatcat:aolboxx22ffozaavisgrscnwf4