On rational co-Hopf G-spaces
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).
rational homotopy associative co-H- spaces
right inverse to the Hurewicz homomorphism
G-homotopy equivalent to a wedge of Moore G-spaces
scientific article; zbMATH DE number 4034652
scientific article