On decomposable H- and co-H-spaces
type: Item
instance of: scholarly article
title: On decomposable H- and co-H-spaces
zbMATH Open document ID: 0605.55011
DOI: 10.1016/0040-9383(86)90032-7
published in: Topology
publication date: 1986-01-01T00:00:00Z
review text: Let R be a subring of \({\mathbb{Q}}\). If X is a nilpotent space, \(X_ R\) denotes the localization of X. Let \(\Omega^ n_ R\) be \(S^ n\) if n odd and \(\Omega \Sigma S^ n_ R\) if n even, \(n>0\). An H-space E is called ''decomposable over R'', if it is equivalent to a weak product of spaces \(\Omega^ n_ R\). The author proves: let E be group like decomposable and of finite type over R. Let X be connected, finite dimensional. Then [X,E] is isomorphic to the group \(\exp ([X,\Omega^*_ R],\Pi_*(E))\) defined by \textit{H. J. Baues} [Commutator calculus and groups of homotopy classes (1981; Zbl 0473.55001)]. A dual statement for cogroup like spaces is also obtained.
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 55P45
Mathematics Subject Classification ID: 55P62
zbMATH DE Number: 3977928
zbMATH Keywords: group like spaces
zbMATH Keywords: nilpotent space
zbMATH Keywords: localization
zbMATH Keywords: H-space
zbMATH Keywords: decomposable
zbMATH Keywords: cogroup like spaces
author: Hans Scheerer
reviewed by: Jean-Claude Thomas
MaRDI profile type: Publication
full work available at URL: 0040-9383(86)90032-7
OpenAlex ID: W2090993362
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description: scientific article; zbMATH DE number 3977928