On decomposable H- and co-H-spaces
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.
scientific article; zbMATH DE number 3977928