Effective finiteness of irreducible Heegaard splittings of non-Haken 3-manifolds

Abstract

The main result is a short effective proof of Tao Li's theorem that a closed non-Haken hyperbolic 3-manifolds. N has at most finitely many irreducible Heegaard splittings. Along the way we show that N has finitely many branched surfaces of pinched negative sectional curvature carrying all closed index-≤ 1 minimal surfaces. This effective result, together with the sequel with Daniel Ketover, solves the classification problem for Heegaard splittings of non-Haken hyperbolic 3-manifolds. Keywords: Heegaard splitting; 3-manifold; lamination; hyperbolic; minimal surface