Fibred knots and disks with clasps
type: Item
instance of: scholarly article
title: Fibred knots and disks with clasps
zbMATH Open document ID: 0578.57004
DOI: 10.1007/BF01458613
published in: Mathematische Annalen
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164158
review text: If K is a null-homotopic knot in a closed, orientable 3-manifold M, then K bounds a disk-with-clasps and is therefore null-homotopic in a handlebody in M. Using the fact that M contains a fibred knot, it is shown that if every knot in M is null-homotopic in a handlebody of genus 2 then M is homeomorphic to \(S^ 3\). This generalizes results of \textit{R. H. Bing} [Ann. Math., II. Ser. 68, 17-37 (1958; Zbl 0081.392)] and \textit{D. R. McMillan} jun. [Trans. Am. Math. Soc. 98, 350-367 (1961; Zbl 0098.147)] where the same conclusion is obtained with the handlebody of genus 2 replaced by a 3-ball and solid torus respectively.
Mathematics Subject Classification ID: 57M40
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M35
zbMATH DE Number: 3925806
zbMATH Keywords: null-homotopic knot in a closed, orientable 3-manifold
zbMATH Keywords: disk-with-clasps
zbMATH Keywords: fibred knot
zbMATH Keywords: null-homotopic in a handlebody of genus 2
author: Cameron McA. Gordon
author: José María Montesinos-Amilibia
MaRDI profile type: Publication
cites work: Necessary and sufficient conditions that a 3-manifold be \(S^3\)
cites work: On the imbedding of polyhedra in 3-space
cites work: On Homologically Trivial 3-Manifolds
cites work: Q3733804
cites work: Simple Knots in Compact, Orientable 3-Manifolds
description: scientific article; zbMATH DE number 3925806