The connective real<i>K</i>–theory of Brown–Gitler spectra

Pearson, Paul

doi:10.2140/agt.2014.14.597

Algebr. Geom. Topol.

2014

DOI: 10.2140/agt.2014.14.597

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The connective realK–theory of Brown–Gitler spectra

Paul Pearson

Abstract: We calculate the connective real K-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 -spectrum for topological real K-theory.

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2015

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The mod 2 Hopf ring for connective Morava K-theory

Pearson

2015

J. Homotopy Relat. Struct.

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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.

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The mod 2 Hopf ring for connective Morava K-theory

Pearson

2015

J. Homotopy Relat. Struct.

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Truncated projective spaces, Brown–Gitler spectra and indecomposable A(1)-modules

Powell

2015

Topology and its Applications

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A structure theorem for bounded-below modules over the subalgebra A (1) of the mod 2 Steenrod algebra generated by Sq 1 , Sq 2 is proved; this is applied to prove a classification theorem for a family of indecomposable A (1)-modules. The action of the A (1)-Picard group on this family is described, as is the behaviour of duality.The cohomology of dual Brown-Gitler spectra is identified within this family and the relation with members of the A (1)-Picard group is made explicit. Similarly, the cohomology of truncated projective spaces is considered within this classification; this leads to a conceptual understanding of various results within the literature. In particular, a unified approach to Ext-groups relevant to Adams spectral sequence calculations is obtained, englobing earlier results of Davis (for truncated projective spaces) and recent work of Pearson (for Brown-Gitler spectrum).2000 Mathematics Subject Classification. 19L41; 55S10. Key words and phrases. Steenrod algebra, indecomposable module, truncated projective space, Brown-Gitler spectra.The author is very grateful to an anonymous referee for remarks which have lead to an improvement in the presentation of the paper.

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The connective realK–theory of Brown–Gitler spectra

Abstract: We calculate the connective real K-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 -spectrum for topological real K-theory.

Cited by 2 publications

References 21 publications

The mod 2 Hopf ring for connective Morava K-theory

The mod 2 Hopf ring for connective Morava K-theory

Truncated projective spaces, Brown–Gitler spectra and indecomposable A(1)-modules

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