Fundamental theorems in global knot theory. I
type: Item
instance of: scholarly article
title: Fundamental theorems in global knot theory. I
zbMATH Open document ID: 0569.57016
author: Itiro Tamura
published in: Proceedings of the Japan Academy. Series A
publication date: 1983-01-01T00:00:00Z
review text: This is an announcement of results on smooth codimension two knotted spheres in closed manifolds M. 1) Seifert surfaces exist, when homologically possible, and have connectivity as high as allowed by the homotopy of the complement of the knot in M. 2) Fibred knots exist in highly connected M - in particular in \(S^ n\times S^{n+1}\). This latter example is null-homotopic but not local, i.e. contained in a ball. 3) Criteria are given in terms of the homology of the infinite cyclic covering of the complement, when M is highly connected, for certain classes of knots to be local or to be unknotted. \(\{\) For part II, see the following review.\(\}\).
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 57Q45
zbMATH DE Number: 3909354
zbMATH Keywords: smooth codimension two knotted spheres in closed manifolds
zbMATH Keywords: Seifert surfaces
zbMATH Keywords: homotopy of the complement of the knot
zbMATH Keywords: Fibred knots
zbMATH Keywords: infinite cyclic covering of the complement
reviewed by: Jerome Levine
MaRDI profile type: Publication
full work available at URL: pjaa.59.446
OpenAlex ID: W2036842262
cites work: Intersection theory of manifolds with operators with applications to knot theory
cites work: Unknotting spheres in codimension two
cites work: On Dehn's lemma and the asphericity of knots
cites work: Foliations and spinnable structures on manifolds
cites work: Unknotted codimension one spheres in smooth manifolds
cites work: Fundamental theorems in global knot theory. II
DOI: 10.3792/PJAA.59.446
description: scientific article; zbMATH DE number 3909354