On the cohomology of stable two stage Postnikov systems

Abstract

We study the cohomology of certain fibre spaces. The spaces are the total spaces of stable two stage Postnikov systems. We study their cohomology as Hopf algebras over the Steenrod algebra. The first theorem determines the cohomology as a Hopf algebra over the ground field, the algebra structure being known previously. The second theorem relates the action of the Steenrod algebra to the Hopf algebra structure and other available structures. The work is in the direction of explicit computations of these structures but is not quite complete with regard to the action of the Steenrod algebra. The ideas of Massey and Peterson [7], Mem. Amer. Math. Soc. No. 74, are used extensively, and $\bmod 2$ cohomology is used throughout.