Volume 14, issue 5 (2014)

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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–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/