Dehn surgery on arborescent knots

Wu, Ying-Qing

doi:10.4310/jdg/1214457901

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2000

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Cited by 63 publications

(67 citation statements)

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“…By [Wu1] there is no reducible surgery on hyperbolic Montesinos knots, so the following result follows immediately from Theorem 1.1 and the classification of toroidal surgeries on these knots [Wu3, Theorem 1.1].…”

Section: Introductionmentioning

confidence: 99%

Immersed surfaces and Seifert fibered surgery on Montesinos knots

2012

Trans. Amer. Math. Soc.

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Section: Introductionmentioning

confidence: 99%

Immersed surfaces and Seifert fibered surgery on Montesinos knots

2012

Trans. Amer. Math. Soc.

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“…On the other hand, many knots have meridionally compressible surface which become compressible after all integral slope Dehn surgery. See for example, [15,Theorem 4.8]. For an accidental surface with an integral accidental slope γ, it become compressible in the manifold obtained by γ -Dehn surgery if and only if the geometric intersection number of γ and γ is less than zero or one [4, Theorem 2.…”

Section: Remarkmentioning

confidence: 99%

Accidental surfaces in knot complements

Ichihara

Ozawa

2000

J. Knot Theory Ramifications

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It is well known that for many knot classes in the 3-sphere, every closed incompressible surface in their complements contains an essential loop which is isotopic into the boundary of the knot exterior. In this paper, we investigate closed incompressible surfaces in knot complements with this property. We show that if a closed, incompressible, non-boundary-parallel surface in a knot complement has such loops, then they determine the unique slope on the boundary of the knot exterior. Moreover, if the slope is non-meridional, then such loops are mutually isotopic in the surface. As an application, a necessary and sufficient condition for knots to bound totally knotted Seifert surfaces is given.

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“…As a direct corollary, together with the result by Wu [25], we have the following. Corollary 1.2 Let K be a hyperbolic arborescent knot.…”

Section: Introductionmentioning

confidence: 78%