#### Volume 14, issue 5 (2014)

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

### Geoffrey Powell

Algebraic & Geometric Topology 14 (2014) 2693–2720
##### 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 $K\phantom{\rule{0.3em}{0ex}}$–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.

##### Keywords
connective $\mathrm{KO}$–theory, detection, Steenrod algebra, elementary abelian group, group cohomology
##### Mathematical Subject Classification 2010
Primary: 19L41, 20J06