Volume 14, issue 5 (2014)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear Contacts ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
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