Heegaard surfaces and measured laminations, II: non-Haken 3-manifolds
Geometric Topology
2007-05-23 v4
Abstract
A famous example of Casson and Gordon shows that a Haken 3-manifold can have an infinite family of irreducible Heegaard splittings with different genera. In this paper, we prove that a closed non-Haken 3-manifold has only finitely many irreducible Heegaard splittings, up to isotopy. This is much stronger than the Waldhausen conjecture. Another immediate corollary is that for any irreducible non-Haken 3-manifold M, there is a number N, such that any two Heegaard splittings of M are equivalent after at most N stabilizations.
Keywords
Cite
@article{arxiv.math/0408199,
title = {Heegaard surfaces and measured laminations, II: non-Haken 3-manifolds},
author = {Tao Li},
journal= {arXiv preprint arXiv:math/0408199},
year = {2007}
}