Strong excision and strong shape invariance are equivalent for homology theories on the category of compact metric pairs
type: Item
instance of: scholarly article
title: Strong excision and strong shape invariance are equivalent for homology theories on the category of compact metric pairs
zbMATH Open document ID: 1145.55009
author: Peter Mrozik
published in: Homology, Homotopy and Applications
publication date: 2008-05-14T00:00:00Z
full work available at URL: n1
review text: In 1960 Milnor gave an axiomatic characterization of Steenrod homology as an ordinary homology theory on the category of compact metric pairs satisfying the strong excision axiom and the cluster axiom. In this paper the author explores the role of the strong excision axiom on its own and proves an interesting result: ``For \(CM^{2}\) the category of compact metric pairs and continuous maps of pairs, a homology theory \( (H_{n},\partial )\) on \(CM^{2}\) is strong shape invariant if and only if it satisfies the strong excision axiom.'' As an application he shows that the homology theory constructed by \textit{L. G. Brown, R. G. Douglas} and \textit{P. A. Fillmore} [Ann. Math. (2) 105, 265--324 (1977; Zbl 0376.46036)] satisfies the strong excision axiom, thus is strong shape invariant.
reviewed by: Corina Mohorianu
Mathematics Subject Classification ID: 55P55
Mathematics Subject Classification ID: 55N20
Mathematics Subject Classification ID: 55N40
zbMATH DE Number: 5274313
zbMATH Keywords: strong shape theory
zbMATH Keywords: strong shape homology theory
zbMATH Keywords: strong excision axiom
MaRDI profile type: Publication
OpenAlex ID: W1984305192
DOI: 10.4310/HHA.2008.V10.N1.A15
description: scientific article