Finiteness properties of self-equivalence groups of rational \(co\)-\(H\)- spaces
type: Item
instance of: scholarly article
title: Finiteness properties of self-equivalence groups of rational \(co\)-\(H\)- spaces
zbMATH Open document ID: 0762.55011
DOI: 10.1007/BF02567745
author: Ken-ichi Maruyama
published in: Manuscripta Mathematica
publication date: 1993-01-17T00:00:00Z
full work available at URL: https://eudml.org/doc/155738
review text: Given a nilpotent complex \(X\) which is rationally a bouquet of spheres, a co-\(H_ 0\)-space, the author investigates finiteness properties involving the group \(E(X)\) of the self-homotopy equivalences of \(X\) and the canonical subgroups \(E_ \pi(X)\) and \(E_ H(X)\), self-equivalences inducing the identity in homotopy and homology respectively. Besides, if \(X\) is 1-connected, explicit formulae for the rank of \(E_ H(X)\) and \(E(X)\) in terms of the rational homotopy and homology of \(X\) are displayed. The author also shows through a list of examples the necessity of \(X\) being finite and that \(E_ \pi(X)\) is not always finite for non co-\(H_ 0\)-spaces.
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 55P10
Mathematics Subject Classification ID: 55P45
zbMATH DE Number: 97881
zbMATH Keywords: nilpotent complex
zbMATH Keywords: co-\(H_ 0\)-space
zbMATH Keywords: self-homotopy equivalences
zbMATH Keywords: rational homotopy
zbMATH Keywords: homology
reviewed by: Francisco Gómez
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 97881