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

Author(s): Tao Li
Journal: J. Amer. Math. Soc. 19 (2006), 625-657.
MSC (2000): Primary 57N10, 57M50; Secondary 57M25
Posted: February 3, 2006
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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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Additional Information:

Tao Li
Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts, 02167-3806
Email: taoli@bc.edu

DOI: 10.1090/S0894-0347-06-00520-0
PII: S 0894-0347(06)00520-0
Keywords: Heegaard splitting, measured lamination, non-Haken 3--manifold
Received by editor(s): November 24, 2004
Posted: February 3, 2006
Additional Notes: Partially supported by NSF grants DMS-0102316 and DMS-0406038
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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