Scharlemann, Martin G. Unknotting number one knots are prime. (English) Zbl 0576.57004 Invent. Math. 82, 37-55 (1985). 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 Cited in 5 ReviewsCited in 39 Documents MSC: 57M25 Knots and links in the \(3\)-sphere (MSC2010) 57N10 Topology of general \(3\)-manifolds (MSC2010) Keywords:prime knot; irreducible 3-manifold; incompressible surface; boundary- compressible 3-manifold; knot of unknotting number one Citations:Zbl 0559.57019 × Cite Format Result Cite Review PDF Full Text: DOI EuDML 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 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.