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Band-sums are ribbon concordant to the connected sum. (English) Zbl 0913.57002

Two knots \(K_1,K_0\) are called ribbon concordant by C. Gordon, \(K_1\geq K_0\), if the height function of a concordance between \(K_1\) and \(K_0\) has no local maxima. It is shown by a simple geometric procedure that any band-connected sum of \(n\) knots is ribbon concordant to the connected sum of these knots. As an application a theorem of Howie and Short follows: If a band-connected sum is a trivial (1-component) knot, then the factors are trivial. The major part of the paper is devoted to the proof of the following: If a bandconnected sum of \(K_1\) and \(K_2\) is fibered, then both \(K_i\) are fibered. The proof uses concepts of Y. Marumoto, A. Thompson and D. Silver.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57Q60 Cobordism and concordance in PL-topology
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