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Unknotting number one knots are prime. (English) Zbl 0576.57004
In this paper it is proved that a knot of unknotting number one is prime; it is a very important work in geometric knot theory. The technique used here is essentially the arguments established by the author [ibid. 79, 125-141 (1985; Zbl 0559.57019)].
Reviewer: M.Yamashita

MSC:
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57N10 Topology of general \(3\)-manifolds (MSC2010)
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References:
[1] [Sc] Scharlemann, M.: Spheres inS 4 with four critical points are standard. Invent. Math.79, 125-141 (1985) · Zbl 0559.57019 · doi:10.1007/BF01388659
[2] [We] Wendt, H.: Die gordische Auflösung von Knoten. Math. Z.42, 680-696 (1937) · Zbl 0016.42005 · doi:10.1007/BF01160103
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