On connective KO–theory of elementary abelian 2–groups

Powell, Geoffrey

doi:10.2140/agt.2014.14.2693

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

Geoffrey Powell

Algebraic & Geometric Topology 14 (2014) 2693–2720

DOI: 10.2140/agt.2014.14.2693

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 $Ω$ –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

References

Publication

Received: 8 March 2013

Revised: 10 February 2014

Accepted: 12 March 2014

Published: 5 November 2014

Authors

Geoffrey Powell
Laboratoire Angevin de Recherche en Mathématiques, UMR 6093 Faculté des Sciences Université d’Angers 2 Boulevard Lavoisier 49045 Angers France
http://math.univ-angers.fr/~powell/

Volume 14, issue 5 (2014)