On the cohomology of stable two stage Postnikov systems

Harper, John R.

doi:10.1090/S0002-9947-1970-0268892-2

On the cohomology of stable two stage Postnikov systems
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by John R. Harper PDF

Trans. Amer. Math. Soc. 152 (1970), 375-388 Request permission

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.

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The $\bmod 2$ cohomology structure of certain fibre spaces

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