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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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
Published electronically: February 3, 2006
MathSciNet review: 2220101
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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: http://dx.doi.org/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
Published electronically: February 3, 2006
Additional Notes: Partially supported by NSF grants DMS-0102316 and DMS-0406038
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.