Cohomology morphisms from $H^ *(B\textrm {U};\textbf {Z}/p)$ to $H^ *(B\textbf {Z}/p;\textbf {Z}/p)$

Abstract:

In this paper we use Hopf algebra and generating function methods to determine the group of all cohomology morphisms from ${H^ * }\left ( {BU;Z/p} \right )$ to ${H^ * }\left ( {BZ/p;Z/p} \right )$ that preserve the Steenrod operations, where $p$ is an odd prime. The group $\left [ {BZ/p,BU} \right ]$ of homotopy classes of maps from $BZ/p$ to BU, which can be calculated directly, is seen to be naturally isomorphic to the group of cohomology morphisms. For $BZ/2$ and BO with coefficients in $Z/2$ there are precisely similar results.