Immersed essential surfaces and Dehn surgery
نویسندگان
چکیده
منابع مشابه
Immersed Surfaces and Dehn Surgery
The problem of how many Dehn fillings on a torus boundary component T of a 3-manifold M will make a closed embedded essential surface F compressible has been settled. A slope β on T is a coannular slope if it is homotopic to some curve on F . As an embedded essential surface, F can have at most one coannular slope. If F has a coannular slope β on T , then by a result of Culler-Gordon-Luecke-Sha...
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Let M be a compact, orientable, irreducible, ∂-irreducible, anannular 3manifold with one component T of ∂M a torus. A slope r on T is a T isotopy class of essential, unoriented, simple closed curves on T , and the distance between two slopes r1 and r2, denoted by 4(r1, r2), is the minimal geometric intersection number among all the curves representing the slopes. For a slope r on T , we denote ...
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A compact orientable surface F with nonnegative Euler characteristic is either a sphere, a disk, a torus, or an annulus. If a 3-manifold M contains such an essential surface, then it is said to be reducible, ∂-reducible, toroidal, or annular, respectively. Any such surface can be used to decompose the manifold further into simpler manifolds. We say that M is a simple manifold if it has no such ...
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We will use immersed surfaces to study Seifert fibered surgery on Montesinos knots, and show that if 1 q1−1 + 1 q2−1 + 1 q3−1 ≤ 1 then a Montesinos knot K(p q1 , p2 q2 , p3 q3 ) admits no atoroidal Seifert fibered surgery.
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ژورنال
عنوان ژورنال: Topology
سال: 2004
ISSN: 0040-9383
DOI: 10.1016/s0040-9383(03)00046-6