Dehn surgery on knots in solid tori creating essential annuli
نویسندگان
چکیده
منابع مشابه
Finite Dehn Surgery on Knots
Let K be a knot with a closed tubular neighbourhood N(K) in a connected orientable closed 3-manifold W , such that the exterior of K, M = W − intN(K), is irreducible. We consider the problem of which Dehn surgeries on K, or equivalently, which Dehn fillings on M , can produce 3-manifolds with finite fundamental group. For convenience, a surgery is called a G-surgery if the resultant 3-manifold ...
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It has been known for over 30 years that every closed connected orientable 3manifold is obtained by surgery on a link in S [8]. However, a classification of such 3-manifolds in terms of this surgery construction has remained elusive. This is due primarily to the lack of uniqueness of the surgery description. In [5], Kirby gave us a calculus of surgery diagrams. However, the lack of a ‘canonical...
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A Dehn surgery on a knot K in S is exceptional if it produces a reducible, toroidal or Seifert fibred manifold. It is known that a large arborescent knot admits no such surgery unless it is a type II arborescent knot. The main theorem of this paper shows that up to isotopy there are exactly three large arborescent knots admitting exceptional surgery, each of which admits exactly one exceptional...
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Suppose K is a hyperbolic knot in a solid torus V intersecting a meridian disk D twice. We will show that if K is not the Whitehead knot and the frontier of a regular neighborhood of K ∪ D is incompressible in the knot exterior, then K admits at most one exceptional surgery, which must be toroidal. Embedding V in S gives infinitely many knots Kn with a slope rn corresponding to a slope r of K i...
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In this paper, we define the primitive/Seifert-fibered property for a knot in S . If satisfied, the property ensures that the knot has a Dehn surgery that yields a small Seifert-fibered space (i.e. base S and three or fewer critical fibers). Next we describe the twisted torus knots, which provide an abundance of examples of primitive/Seifert-fibered knots. By analyzing the twisted torus knots, ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1997
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-97-01723-6