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

Author: Tao Li
Journal: J. Amer. Math. Soc. 19 (2006), 625-657
MSC (2000): Primary 57N10, 57M50; Secondary 57M25
Posted: February 3, 2006
MathSciNet review: 2220101
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Abstract | References | Similar Articles | Additional Information

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 generalized Waldhausen conjecture. Another immediate corollary is that for any irreducible non-Haken 3-manifold , there is a number such that any two Heegaard splittings of are equivalent after at most stabilizations.

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