Banding, twisted ribbon knots, and producing reducible manifolds via Dehn surgery (Q1113487)
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scientific article; zbMATH DE number 4082517
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Banding, twisted ribbon knots, and producing reducible manifolds via Dehn surgery |
scientific article; zbMATH DE number 4082517 |
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Banding, twisted ribbon knots, and producing reducible manifolds via Dehn surgery (English)
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1990
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It is shown that if the unknot can be obtained by attaching a band to a composite knot or link, then that knot or link must have a summand of bridge number two. The principal corollaries are that a composite twisted ribbon number one knot has a two-bridge summand, that reducible manifolds arising from Dehn surgery on a strongly invertible knot have lens space summands, and that homology spheres arising from Dehn surgery on a strongly invertible knot are prime.
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attaching a band to a composite knot
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summand of bridge number two
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composite twisted ribbon number one knot
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Dehn surgery
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strongly invertible knot
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lens space
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homology spheres
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