Algebraic K-theory of spaces, with bounded control
type: Item
instance of: scholarly article
title: Algebraic K-theory of spaces, with bounded control
zbMATH Open document ID: 0722.19002
DOI: 10.1007/BF02391904
author: Wolrad Vogell
published in: Acta Mathematica
publication date: 1990-01-01T00:00:00Z
review text: The algebraic K-theory A(X) of a space X is constructed from a category of spaces over X and homotopy equivalences between them. The author constructs a controlled analogue A(X;B), given a metric space B; it is constructed from spaces over \(X\times B\) and bounded homotopy equivalences. The main result is that the functor \(K\mapsto A(X;o(K))\) is a homology theory on piecewise linear subcomplexes of \({\mathbb{R}}^{\infty}\); here o(K) denotes an open cone on K. As a special case, it is shown that \(A(X;{\mathbb{R}}^ n)\) gives a non-connected n-fold delooping of A(X).
reviewed by: Richard John Steiner
Mathematics Subject Classification ID: 19D10
Mathematics Subject Classification ID: 55P47
zbMATH DE Number: 4189998
zbMATH Keywords: controlled algebraic K-theory of spaces
zbMATH Keywords: homology theory on piecewise linear subcomplexes of \({\mathbb{R}}^{\infty }\)
zbMATH Keywords: open cone
zbMATH Keywords: n-fold delooping
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4189998