Short geodesics in hyperbolic 3-manifolds

Abstract

For each g ≥ 2, we prove existence of a computable constant.∈(g)> 0 such that if S is a strongly irreducible Heegaard surface of genus g in a complete hyperbolic 3-manifold M and γ is a simple geodesic of length less than ∈(g) in M, then γ is isotopic into S.