Virtually Haken fillings and semi-bundles
نویسندگان
چکیده
منابع مشابه
Haken fillings and semi - bundles
Suppose that M is a fibered three-manifold whose fiber is a surface of positive genus with one boundary component. Assume that M is not a semi-bundle. We show that infinitely many fillings of M along ∂M are virtually Haken. Combined with a result of Cooper and Long, this gives the corollary that infinitely many fillings of the complement of any non-trivial knot in a Z-homology three-sphere are ...
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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...
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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 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 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: Geometry & Topology
سال: 2006
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2006.10.2237