On connective $\mathrm{KO}$–theory of elementary abelian $2$–groups

Abstract

A general notion of detection is introduced and used in the study of the cohomology of elementary abelian $2$–groups with respect to the spectra in the Postnikov tower of orthogonal $K$–theory. This recovers and extends results of Bruner and Greenlees and is related to calculations of the (co)homology of the spaces of the associated $\Omega$–spectra by Stong and by Cowen Morton.