Essential laminations and Dehn surgery on 2-bridge knots
نویسندگان
چکیده
منابع مشابه
Sutured Manifold Hierarchies, Essential Laminations, and Dehn Surgery
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 ...
متن کاملThe Classification of Dehn Surgeries on 2-bridge Knots
We will determine whether a given surgery on a 2-bridge knot is reducible, toroidal, Seifert bered, or hyperbolic. In [Th1] Thurston showed that if K is a hyperbolic knot, then all but nitely many surgeries on K are hyperbolic. In particular, for the Figure 8 knot, it was shown that exactly 9 nontrivial surgeries are non-hyperbolic. Let Kp=q be a 2-bridge knot associated to the rational number ...
متن کاملThe Classification of Exceptional Dehn Surgeries on 2-bridge Knots
A nontrivial Dehn surgery on a hyperbolic knot K in S is exceptional if the resulting manifold is either reducible, or toroidal, or a Seifert fibered manifold whose orbifold is a sphere with at most three exceptional fibers, called a small Seifert fibered space. Thus an exceptional Dehn surgery is non-hyperbolic, and using a version of Thurston’s orbifold theorem proved by Boileau and Porti [BP...
متن کاملFinite 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 ...
متن کاملSmall Seifert- bered spaces and Dehn surgery on 2-bridge knots
We show that non-integer surgery on a non-torus 2-bridge knot can never yield a small Seifertbered space. In most cases, no surgery will yield a small Seifertbered space.
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1995
ISSN: 0166-8641
DOI: 10.1016/0166-8641(95)00085-u