Essential laminations and Haken normal form
نویسندگان
چکیده
منابع مشابه
Essential Laminations and Haken Normal Form
0. Introduction. The notion of (Haken) normal form w.r.t. a triangulation of a 3-manifold traces back to Kneser's work in the 1930's on surfaces in 3-manifolds. Haken studied it extensively in the 1960's, and showed [8] how to use it to create nite algorithms for the determination of various properties of embedded surfaces. This has since culminated, in the work of Jaco and Oertel [10], in an a...
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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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Roussarie and Thurston [Ro], [Th] showed that given a taut foliation F and an incompressible torus T in a 3-manifold M , the torus may be isotoped so that it is either transverse to the leaves of the foliation, or is equal to one of the leaves of the foliation. This result was known to be false in the more general context of a foliation F without Reeb components. The only obstruction, however [...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1995
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1995.168.217