On the mod-2 cohomology of some 2-Postnikov towers

TL;DR

This paper investigates the mod-2 cohomology of certain 2-Postnikov towers, utilizing tools like Lannes' T functor and the Eilenberg-Moore spectral sequence to analyze fiber cohomology.

Contribution

It provides new results on the mod-2 cohomology of fibers in specific decomposable maps, highlighting the use of advanced spectral sequence techniques.

Findings

Identifies the mod-2 cohomology structure of certain fibers

Demonstrates the application of Lannes' T functor and Eilenberg-Moore spectral sequence

Offers insights into the nilpotent elements in cohomology

Abstract

The present note presents some results about the mod-2 cohomology, modulo nilpotent elements elements of the fiber E of a decomposable map $\psi$ : K(Z, 2) $\rightarrow$ K(Z/2, p). This is more an announcement and a brief description of the tools that are used: Lannes' T functor and the Eilenberg-Moore spectral sequence.