A correction to a paper of H. King
type: Item
instance of: scholarly article
title: A correction to a paper of H. King
zbMATH Open document ID: 0619.57004
DOI: 10.1007/BF01388916
author: Les Reid
published in: Inventiones Mathematicae
publication date: 1987-01-01T00:00:00Z
review text: In his paper [ibid. 37, 193-199 (1976; Zbl 0318.57037)], \textit{H. C. King} shows that a conjecture of Thom is false, if one can find a smooth compact connected n-dimensional submanifold N of \(S^ n\) such that \(NK_ 0({\mathbb{Z}}[\pi_ 1N])\neq 0\) and \(\tilde K_ 0({\mathbb{Z}}[\pi_ 1(\partial N\times S^ 1)])=0\). His candidate had \(\pi_ 1N={\mathbb{Z}}_ 2\oplus {\mathbb{Z}}_ 2\), \(\partial N=\partial_ 1N\cup^{.}\partial_ 2N\), \(\partial_ iN\) connected and \(\pi_ 1(\partial_ iN)={\mathbb{Z}}_ 2\), \(i=1,2\). Such a manifold doesn't exist, but one having the desired properties can be constructed.
Mathematics Subject Classification ID: 57N15
Mathematics Subject Classification ID: 57Q10
Mathematics Subject Classification ID: 57R45
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
zbMATH DE Number: 4005156
zbMATH Keywords: homeomorphism class of a germ of a submanifold
zbMATH Keywords: homeomorphism type of a germ of an analytic map
zbMATH Keywords: projective class group
zbMATH Keywords: group ring of fundamental group
MaRDI profile type: Publication
cites work: Q5620675
cites work: A quick trip through knot theory
full work available at URL: https://doi.org/10.1007/bf01388916
OpenAlex ID: W2069232203
description: scientific article; zbMATH DE number 4005156