The mod 2 Hopf ring for connective Morava K-theory

Abstract

This paper examines the mod 2 homology of the spaces in the Omegaspectrum for connective Morava K -theory, i.e., the mod 2 Hopf ring for connective Morava K -theory. A natural set of generators for this Hopf ring arising from the homology and homotopy of the connective Morava K -theory spectrum is calculated and the non-trivial circle product relations among the generators arising from homology and homotopy are determined. This Hopf ring calculation is accomplished using Dieudonné ring theory and Adams spectral sequences for the connective Morava Ktheory of Brown-Gitler spectra.