Heegaard surfaces and measured laminations, II: Non-Haken 3–manifolds
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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 $M$, there is a number $N$ such that any two Heegaard splittings of $M$ are equivalent after at most $N$ stabilizations.
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- Tao Li
- Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts, 02167-3806
- Email: email@example.com
- Received by editor(s): November 24, 2004
- Published electronically: February 3, 2006
- Additional Notes: Partially supported by NSF grants DMS-0102316 and DMS-0406038
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: J. Amer. Math. Soc. 19 (2006), 625-657
- MSC (2000): Primary 57N10, 57M50; Secondary 57M25
- DOI: https://doi.org/10.1090/S0894-0347-06-00520-0
- MathSciNet review: 2220101