Heegaard surfaces and measured laminations, II: non-Haken 3-manifolds

Details Heegaard surfaces and measured laminations, II: non-Haken 3-manifolds Heegaard surfaces and measured laminations, II: non-Haken 3-manifolds

2004-08-15

arxiv.org/abs/math/0408199v4

J. Amer. Math. Soc., 19 (2006) 625-657

Mathematics

Geometric Topology

Scientific paper

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.

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