The Omega spectrum for mod 2 KO-theory

The 8-periodic theory that comes from the $KO$ -theory of the mod 2 Moore space is the same as the real first Morava $K$ -theory obtained from the homotopy fixed points of the $ℤ ∕ (2)$ action on the first Morava $K$ -theory. The first Morava $K$ -theory, $K (1)$ , is just mod 2 $KU$ -theory. We compute the homology Hopf algebras for the spaces in this Omega spectrum.

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Keywords

$K\mkern-2mu$-theory, homology, Omega spectra

Mathematical Subject Classification 2010

Primary: 55N15, 55P47, 55R20, 55T20

Supplementary material

The Omega spectrum for mod 2 KO-theory: appendix

Milestones

Received: 8 August 2019

Revised: 17 November 2019

Accepted: 9 December 2019

Published: 20 June 2020

Authors

W. Stephen Wilson
Department of Mathematics Johns Hopkins University Baltimore, MD United States

Vol. 5, No. 2, 2020

W. Stephen Wilson

Abstract