Reduced Powers of Cohomology Classes

We shall present a set of new operations which interrelate the elements of the various dimensional cohomology groups of a space. They are topologically invariant, and provide sharper methods for distinguishing topological types and homotopy types of spaces. They are generalizations of the squaring operations introduced in [4]. Let H'(K;G) denote the qth cohomology group of a complex K with coefficient group G. Let integers q, i be given, and let G, G' be fixed coefficient groups. Then a cohomology operation, relative to (q,iGG'), is a mapping