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On composite twisted unknots. (English) Zbl 0883.57004

Summary: Following Y. Mathieu [Knots 90, Proc. Int. Conf. Knot Theory Rel. Topics, Osaka/Japan 1990, 93-102 (1992; Zbl 0772.57012)], K. Motegi [Proc. Am. Math. Soc. 119, No. 3, 979-983 (1993; Zbl 0808.57003)] and others, we consider the class of possible composite twisted unknots as well as pairs of composite knots related by twisting. At most one composite knot can arise from a particular \(V\)-twisting of an unknot; moreover a twisting of the unknot cannot be composite if we have applied more than a single full twist. A pair of composite knots can be related through at most one full twist for a particular \(V\)-twisting, or one summand was unaffected by the twist, or the knots were the right and left handed granny knots. Finally a conjectured characterization of all composite twisted unknots that do arise is given.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
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References:

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