On connective KO-theory of elementary abelian 2-groups

TL;DR

This paper introduces a new detection method in the cohomology of elementary abelian 2-groups, extending previous results and connecting to calculations involving orthogonal K-theory spectra.

Contribution

It develops a general notion of detection applied to the cohomology of elementary abelian 2-groups within orthogonal K-theory spectra, extending prior work by Bruner, Greenlees, Stong, and Cowen Morton.

Findings

Extended the understanding of cohomology detection in elementary abelian 2-groups.

Connected detection methods to calculations of (co)homology of Omega-spectra spaces.

Reproduced and generalized previous results in the field.

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 Omega-spectra by Stong and by Cowen Morton.