On \(K_ 1\)-theory of the Euclidean space
type: Item
instance of: scholarly article
title: On \(K_ 1\)-theory of the Euclidean space
zbMATH Open document ID: 0611.18007
DOI: 10.1016/0166-8641(86)90035-0
author: William P. Thurston
author: L. N. Vaserstein
published in: Topology and its Applications
publication date: 1986-01-01T00:00:00Z
review text: It is shown that any \(n\) by \(n\) matrix of determinant 1, \(n\geq 3\), whose entries are continuous real functions of \(N=3\) variables, can be reduced to the identity matrix by addition operations (with continuous coefficients). In the case \(n=2\), this is not true. The case of \(N=1\) was done in a previous paper by a different method. The case of arbitrary \(N\) is finished by a different method in a paper to appear in Proc. Am. Math. Soc. The similar result for polynomial functions (n\(\geq 3)\) is due to A. Suslin.
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 3987533
zbMATH Keywords: \(K_ 1\) of ring of continuous functions of three variables
zbMATH Keywords: algebraic K- theory of rings of continuous functions
zbMATH Keywords: Stone-Čech compactification on the Euclidean space
zbMATH Keywords: cohomotopy groups
zbMATH Keywords: vector fields
MaRDI profile type: Publication
full work available at URL: 0166-8641(86)90035-0
OpenAlex ID: W2015650420
cites work: \(K\)-theory and stable algebra
cites work: Stable rank of rings and dimensionality of topological spaces
cites work: Vector Bundles and Projective Modules
description: scientific article; zbMATH DE number 3987533