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Tangle decompositions of doubled knots. (English) Zbl 0912.57004
Let \(K\) be a doubled knot of a knot \(K_1\). \(K_1\) is called the companion knot of \(K\). If a decomposing 2-sphere divides \(K\) in two essential tangles with \(m\) strings, then it is proved that \(m\) is even and the same 2-sphere divides the companion \(K_1\) in two essential tangles with \(m/2\) strings. As a corollary, if \(K_1\) is \(n\)-string prime for every \(n\geq 1\) then so is \(K\).
Reviewer: D.Erle (Dortmund)
MSC:
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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