Cohomology theories on compact and locally compact spaces
type: Item
instance of: scholarly article
title: Cohomology theories on compact and locally compact spaces
zbMATH Open document ID: 0605.55004
DOI: 10.4171/RMI/24
published in: Revista Matemática Iberoamericana
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/39300
review text: The aim of this paper is to give an expository account of the uniqueness theorem for cohomology theories on the category of locally compact Hausdorff spaces and proper continuous functions. The uniqueness theorem can be applied to give a proof of the known result that the Chern character induces an isomorphism K(X)\(\otimes {\mathbb{Q}}\cong \check H^{even}(X; {\mathbb{Q}})\) for every locally compact space X. The uniqueness theorem is also used to give a new proof of the duality theorem in stable homotopy theory: \(\{A;S^ n-B\}^ q\cong \{B;S^ n-A\}^ q\) where A,B are compact subsets of \(S^ n\).
reviewed by: Rolf Kultze
Mathematics Subject Classification ID: 55N40
Mathematics Subject Classification ID: 55P25
Mathematics Subject Classification ID: 55R50
Mathematics Subject Classification ID: 55N15
zbMATH DE Number: 3977921
zbMATH Keywords: uniqueness theorem for cohomology theories on the category of locally compact Hausdorff spaces
zbMATH Keywords: Chern character
zbMATH Keywords: duality theorem in stable homotopy theory
author: Edwin H. Spanier
MaRDI profile type: Publication
OpenAlex ID: W1974367142
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description: scientific article; zbMATH DE number 3977921