On rational co-Hopf G-spaces
type: Item
instance of: scholarly article
title: On rational co-Hopf G-spaces
zbMATH Open document ID: 0635.55012
DOI: 10.1007/BF01179271
author: Ryszard Doman
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173867
review text: Let G be a finite group. The author is working in the category f pointed simply connected spaces (resp. G-spaces) of the homotopy type of complexes (resp. G-complexes). Using a result of I. Bernstein he shows that on the category of rational homotopy associative co-H-spaces and co- H-maps there exists a functorial right inverse to the Hurewicz homomorphism. As a consequence, if C is a rational G-co-H-space, then the equivariant Hurewicz map \(\pi_*(C)\to H_*(C)\) has a right inverse (in the equivariant setting). If, in addition, proj dim \(H_ n(C)\leq 1\) for all \(n\geq 2\), then C is G- homotopy equivalent to a wedge of Moore G-spaces (note that by a result of P. J. Kahn a rational G-co-H-space not always decomposes as a wedge of Moore G-spaces).
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 55P45
Mathematics Subject Classification ID: 55P91
zbMATH DE Number: 4034652
zbMATH Keywords: equivariant co-H-space
zbMATH Keywords: finite group
zbMATH Keywords: rational homotopy associative co-H- spaces
zbMATH Keywords: right inverse to the Hurewicz homomorphism
zbMATH Keywords: equivariant Hurewicz map
zbMATH Keywords: G-homotopy equivalent to a wedge of Moore G-spaces
reviewed by: Hans Scheerer
MaRDI profile type: Publication
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cites work: On rationalized H- and co-H-spaces. With an appendix on decomposable H- and co-H-spaces
cites work: Rationalization of Hopf G-spaces
cites work: Equivariant Homotopy Theory and Milnor's Theorem
OpenAlex ID: W2086732266
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description: scientific article; zbMATH DE number 4034652