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Banding, twisted ribbon knots, and producing reducible manifolds via Dehn surgery. (English) Zbl 0662.57004

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.
Reviewer: S.A.Bleiler

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57N10 Topology of general \(3\)-manifolds (MSC2010)
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References:

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