On connective KO–theory of elementary abelian 2–groups

Powell, Geoffrey¹

¹Laboratoire Angevin de Recherche en Mathématiques, UMR 6093, Faculté des Sciences, Université d’Angers, 2 Boulevard Lavoisier, 49045 Angers, France

Algebraic and Geometric Topology, Tome 14 (2014) no. 5, pp. 2693-2720

Résumé

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.

Détail

DOI : 10.2140/agt.2014.14.2693

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

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