Unknotting number one knots are prime
type: Item
instance of: scholarly article
title: Unknotting number one knots are prime
zbMATH Open document ID: 0576.57004
DOI: 10.1007/BF01394778
author: Martin Scharlemann
published in: Inventiones Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143276
review text: 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)].
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 3921530
zbMATH Keywords: prime knot
zbMATH Keywords: irreducible 3-manifold
zbMATH Keywords: incompressible surface
zbMATH Keywords: boundary- compressible 3-manifold
zbMATH Keywords: knot of unknotting number one
MaRDI profile type: Publication
cites work: Smooth spheres in \({\mathbb{R}}^ 4\) with four critical points are standard
cites work: Die gordische Auflösung von Knoten
OpenAlex ID: W1994099170
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description: scientific article; zbMATH DE number 3921530