Strongly irreducible Heegaard splittings of hyperbolic 3-manifolds

Abstract

Colding and Gabai have given an effective version of Li's theorem that non-Haken hyperbolic 3-manifolds have finitely many irreducible Heegaard splittings. As a corollary of their work, we show that Haken hyperbolic 3-manifolds have a finite collection of strongly irreducible Heegaard surfaces $S_i$ and incompressible surfaces $K_j$ such that any strongly irreducible Heegaard surface is a Haken sum $S_i+{\sum }_j{n}_j{K}_j$, up to one-sided associates of the Heegaard surfaces.

3 pages. Accepted for publication in Proceedings of AMS

References in corpus (1)

• Effective Finiteness of irreducible Heegaard splittings of non Haken 3-manifolds