A geometric decomposition of spaces into cells of different types. II: Homology theory
type: Item
instance of: scholarly article
title: A geometric decomposition of spaces into cells of different types. II: Homology theory
zbMATH Open document ID: 1149.55013
author: Elias Gabriel Minian
author: Miguel Ottina
published in: Topology and its Applications
publication date: 2008-09-23T00:00:00Z
review text: In an earlier paper [J. Homotopy Relat. Struct. 1, No. 1, 245--271, electronic only (2006; Zbl 1129.55005)], the authors introduced the notion of a \(CW(A)\)-complex. This is a space that is built up from \(A\)-cells. The paper considers the homology of these complexes. They show that in the case where the homology of \(A\) is concentrated in one dimension and in the case where the homology of \(A\) is free there is a chain complex constructed from the homology of \(A\) using the \(A\) cells as generators whose homology is that of the complex.
Mathematics Subject Classification ID: 55U10
Mathematics Subject Classification ID: 57Q05
Mathematics Subject Classification ID: 18G35
Mathematics Subject Classification ID: 18G55
zbMATH DE Number: 5346279
zbMATH Keywords: \(CW(A)\)-complex
zbMATH Keywords: homology
zbMATH Keywords: pushout
reviewed by: Jonathan Hodgson
MaRDI profile type: Publication
full work available at URL: j.topol.2008.05.015
OpenAlex ID: W2041992732
cites work: Q4040829
cites work: Q5200638
cites work: A generalization of the triad theorem of Blakers-Massey
cites work: Cellular spaces, null spaces and homotopy localization
cites work: Q3995201
cites work: Complexes in Cat
cites work: A geometric decomposition of spaces into cells of different types
cites work: Computing spectral sequences
DOI: 10.1016/J.TOPOL.2008.05.015
description: scientific article; zbMATH DE number 5346279