LIFTED HEEGAARD SURFACES AND VIRTUALLY HAKEN MANIFOLDS
نویسندگان
چکیده
منابع مشابه
Heegaard splittings and virtually Haken Dehn filling
A compact connected 3-manifold is said to be virtually Haken if it has a finite sheeted covering space which is Haken. The virtual Haken conjecture states that every compact, connected, orientable, irreducible 3-manifold with infinite fundamental group is virtually Haken. Since virtually Haken 3-manifolds and Haken 3-manifolds possess similar properties, such as geometric decompositions and, in...
متن کاملHeegaard 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...
متن کاملHeegaard Splittings, the Virtually Haken Conjecture and Property (τ )
The behaviour of finite covers of 3-manifolds is a very important, but poorly understood, topic. There are three, increasingly strong, conjectures in the field that have remained open for over twenty years – the virtually Haken conjecture, the positive virtual b 1 conjecture and the virtually fibred conjecture. Any of these would have many ramifications for 3-manifold theory. In this paper, we ...
متن کاملVirtually Haken Dehn--lling
We show that \most" Dehn-llings of a non-bered, atoroidal, Haken three-manifold with torus boundary are virtually Haken. 1 Results Suppose that X is a compact, oriented, three-manifold with boundary a torus T: We will pick a basis of H 1 (T) represented by simple loops ; such that = 0 in H 1 (X; Q): We call a longitude and a meridian. A slope, ; on T is the isotopy class of essential unoriented...
متن کاملS ep 2 00 5 HEEGAARD SPLITTINGS , THE VIRTUALLY HAKEN CONJECTURE AND PROPERTY ( τ ) MARC LACKENBY
The behaviour of finite covers of 3-manifolds is a very important, but poorly understood, topic. There are three, increasingly strong, conjectures in the field that have remained open for over twenty years – the virtually Haken conjecture, the positive virtual b 1 conjecture and the virtually fibred conjecture. Any of these would have profound ramifications for 3-manifold theory. In this paper,...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2012
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216512500733