The knots in D2 × S1 which have nontrivial Dehn surgeries that yield D2 × S1
نویسندگان
چکیده
منابع مشابه
Dehn surgeries that yield fibred 3 - manifolds
We study Dehn surgeries on null-homotopic knots that yield fibred 3-manifolds when an additional (but natural) homological restriction is imposed. The major tool used is Gabai’s theory of sutured manifold decomposition. Such surgeries are negative examples to a question of Michel Boileau. Another result we will prove is about surgeries which reduce the Thurston norm of a fibred manifold.
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We show that if a surgery on a knot in a product sutured manifold yields the same product sutured manifold, then this knot is a 0or 1-crossing knot. The proof uses techniques from sutured manifold theory.
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A 3-manifold is ∂-reducible if ∂M is compressible in M . By definition, this means that there is a disk D properly embedded in M so that ∂D is an essential curve in ∂M . The disk D is called a compressing disk of ∂M , or a ∂-reducing disk of M . Now suppose M is a ∂-reducible manifold. Let K be a knot in a 3-manifold M such that ∂M is incompressible in M − K. A Dehn surgery on K is called ∂-red...
متن کاملThe Classification of Toroidal Dehn Surgeries on Montesinos Knots
Exceptional Dehn surgeries have been classified for 2-bridge knots and Montesinos knots of length at least 4. In this paper we classify all toroidal Dehn surgeries on Montesinos knots of length 3.
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 ...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1991
ISSN: 0166-8641
DOI: 10.1016/0166-8641(91)90037-m