On the classification of Heegaard splittings

TL;DR

This paper solves the classification problem for irreducible Heegaard surfaces in non Haken hyperbolic 3-manifolds, providing a complete list up to isotopy, advancing understanding in 3-manifold topology.

Contribution

It offers a complete classification of irreducible Heegaard splittings for a significant class of 3-manifolds, which was previously unresolved.

Findings

Classification achieved for non Haken hyperbolic 3-manifolds

Complete list of irreducible Heegaard surfaces provided

Advances the understanding of 3-manifold topology

Abstract

The long standing classification problem in the theory of Heegaard splittings of 3-manifolds is to exhibit for each closed 3-manifold a complete list, without duplication, of all its irreducible Heegaard surfaces, up to isotopy. We solve this problem for non Haken hyperbolic 3-manifolds.