Volume 14, issue 1 (2014)

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The connective real $K\!$–theory of Brown–Gitler spectra

Paul Thomas Pearson

Algebraic & Geometric Topology 14 (2014) 597–625
Abstract

We calculate the connective real $K\phantom{\rule{0.3em}{0ex}}$–theory homology of the mod $2$ Brown–Gitler spectra. We use this calculation and the theory of Dieudonné rings and Hopf rings to determine the mod $2$ homology of the spaces in the connective $\Omega$–spectrum for topological real $K\phantom{\rule{0.3em}{0ex}}$–theory.

Keywords
Hopf ring, Dieudonné ring, topological real $K\!$–theory
Primary: 55T25
Secondary: 55P42