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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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