Heegaard Surfaces and Measured Laminations, I: the Walderhausen Conjecture
نویسنده
چکیده
We give a proof of the so-called generalized Walderhausen conjecture, which says that an orientable irreducible atoroidal 3-manifold has only finitely many Heegaard splittings in each genus, up to isotopy. Jaco and Rubinstein have announced a proof of this conjecture using
منابع مشابه
Heegaard Surfaces and Measured Laminations, Ii: Non-haken 3-manifolds
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 Walderhausen conjecture. Another immediate corollary is that for any irreducible n...
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تاریخ انتشار 2004