Knotted homology 3-spheres in \(S^ 5\)
type: Item
instance of: scholarly article
title: Knotted homology 3-spheres in \(S^ 5\)
zbMATH Open document ID: 0618.57008
author: Osamu Saeki
published in: Journal of the Mathematical Society of Japan
publication date: 1988-01-01T00:00:00Z
review text: The isotopy class of a smoothly embedded homology 3-sphere K in \(S^ 5\) is called a simple 3-knot if \(\pi _ 1(S^ 5-K)\cong {\mathbb{Z}}\). Simple 3-knots are classified by their Seifert matrices. Using this classification the author defines a trivial \(\Sigma\)-knot for every homology 3-sphere \(\Sigma\) with zero Rohlin invariant and characterizes it as the unique simple \(\Sigma\)-knot whose complement is homotopy equivalent to \(S^ 1\). Furthermore the following is proved: (1) There exist infinitely many decomposable algebraic 3-knots. (2) There exist a simple fibered 3-knot which is, though decomposable, not the connected sum of two nontrivial fibered 3-knots. (3) Algebraically fibered simple 3-knots are stably fibered.
Mathematics Subject Classification ID: 57Q45
Mathematics Subject Classification ID: 57Q35
zbMATH DE Number: 4003075
zbMATH Keywords: smoothly embedded homology 3-sphere in \(S^ 5\)
zbMATH Keywords: simple 3-knots
zbMATH Keywords: Seifert matrices
zbMATH Keywords: Rohlin invariant
zbMATH Keywords: decomposable algebraic 3-knots
zbMATH Keywords: simple fibered 3-knot
zbMATH Keywords: algebraically fibered simple 3-knots
zbMATH Keywords: stably fibered
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04010065
OpenAlex ID: W2014223904
DOI: 10.2969/JMSJ/04010065
description: scientific article; zbMATH DE number 4003075