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 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 کاملVirtual Haken 3-Manifolds and Dehn Filling
In this paper we consider the conjecture through the Dehn filling construction. LetM be a compact, connected, orientable, irreducible 3-manifold M such that ∂M is a torus. Recall that a slope on ∂M is the isotopy class of an unoriented, simple, essential loop in ∂M . We use ∆(r1, r2) to denote the distance (i.e. the minimal geometric intersection number) between two slopes r1 and r2 on ∂M and u...
متن کاملReducing Dehn filling and toroidal Dehn filling
It is shown that if M is a compact, connected, orientable hyperbolic 3-manifold whose boundary is a torus, and 7‘1, FZ are two slopes on i7M whose associated fillings are respectively a reducible manifold and one containing an essential torus, then the distance between these slopes is bounded above by 4. Under additional hypotheses this bound is improved Consequently the cabling conjecture is s...
متن کاملVirtual Haken 3-manifolds and Dehn "lling
A stronger conjecture is that any closed, connected, orientable, irreducible 3-manifold= with in"nite fundamental group has a virtually positive "rst Betti number, i.e.= has a "nite cover which has positive "rst Betti number. Conjecture 0.1 becomes more compelling due to the recent work of Gabai et al. [16]. In fact it follows from [16] (as well as [9, 12, 13, 32]) that if a closed 3-manifold= ...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1999
ISSN: 0022-040X
DOI: 10.4310/jdg/1214425220