Inequivalent fibred knots whose homotopy Seifert pairings are isometric
type: Item
instance of: scholarly article
title: Inequivalent fibred knots whose homotopy Seifert pairings are isometric
zbMATH Open document ID: 0711.57015
DOI: 10.1007/BF01446596
author: John R. Klein
author: Alexander I. Suciu
published in: Mathematische Annalen
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164805
review text: Using a new spinning construction, we give examples of fibred n-knots, \(n\geq 9\), whose fibres are 1-connected, whose associated homotopy Seifert pairings (in the sense of M. Farber) are isometric, yet whose complements are homotopically distinct. These examples show that knots are not determined by their homotopy Seifert pairings outside of the stable range.
Mathematics Subject Classification ID: 57Q45
zbMATH DE Number: 4169682
zbMATH Keywords: homotopically distinct complements
zbMATH Keywords: spinning construction
zbMATH Keywords: examples of fibred n-knots
zbMATH Keywords: homotopy Seifert pairings
zbMATH Keywords: isometric
MaRDI profile type: Publication
cites work: Isotopy Types of Knots of Codimension Two
cites work: Iterated torus knots
cites work: Blanchfield Duality and Simple Knots
cites work: Some non-stable homotopy groups of Lie groups
cites work: An algebraic classification of some knots of codimension two
cites work: $2$-Primary components of the homotopy groups of some Lie groups
cites work: Spinning knots about submanifolds; spinning knots about projections of knots
cites work: Duality in homotopy theory
cites work: Inequivalent frame-spun knots with the same complement
cites work: Compositional Methods in Homotopy Groups of Spheres. (AM-49)
cites work: On S-equivalence of Seifert matrices
cites work: Q4194139
cites work: Classification problems in differential topology. II: Diffeomorphisms of handlebodies
cites work: Q4192669
OpenAlex ID: W1983498723
description: scientific article; zbMATH DE number 4169682