Hopf rings and unstable operations
Let \({\mathcal C} {\mathcal P}\) denote the full subcategory of the homotopy category of spaces whose objects are finite products of \(\mathbb{C} P^ \infty\)s. Using algebraically defined Hopf rings introduced by \textit{D. C. Ravenel} and \textit{W. S. Wilson} [ibid. 9, 241-280 (1977; Zbl 0373.57020)] the author shows that for good cohomology theories \(E^*\) and \(F^*\) the set of unstable cohomology operations from \(F\) to \(E\) (in even degrees) can be identified with the set of natural transformations from \(F\) to \(E\) when restricted to the category \({\mathcal C} {\mathcal P}\). As an application the author gives a new proof for the existence of \(BP\)- unstable Adams operations.
finite products of \(\mathbb{C} P^ \infty\)s
scientific article; zbMATH DE number 612146