zbMATH — the first resource for mathematics

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

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57N10 Topology of general \(3\)-manifolds (MSC2010)
Full Text: DOI EuDML
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.