Heegaard structures of manifolds in the Dehn filling space
نویسندگان
چکیده
منابع مشابه
Heegaard structures of manifolds in the Dehn "lling space
We prove that after Dehn "lling an incompressible torus in the boundary of an a-cylindrical 3-manifold the Heegaard genus degenerates by at most one for all but "nitely many "llings. We do so by proving that for all but "nitely many "llings the core of the attached solid torus can be isotoped into the minimal Heegaard surface of the "lled manifold, we say that these manifolds are `gooda. For th...
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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...
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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...
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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...
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ژورنال
عنوان ژورنال: Topology
سال: 2000
ISSN: 0040-9383
DOI: 10.1016/s0040-9383(99)00026-9