Homology, Homotopy and Applications

Volume 9 (2007)

Number 2

Beyond the hit problem: Minimal presentations of odd-primary Steenrod modules, with application to $CP(\infty)$ and BU

Pages: 363 – 395

DOI: http://dx.doi.org/10.4310/HHA.2007.v9.n2.a13

Authors

David J. Pengelley (Mathematical Sciences, New Mexico State University, Las Cruces, N.M., U.S.A.)

Frank Williams (Mathematical Sciences, New Mexico State University, Las Cruces, N.M., U.S.A.)

Abstract

We describe a minimal unstable module presentation over the Steenrod algebra for the odd-primary cohomology of infinite-dimensional complex projective space and apply it to obtain a minimal algebra presentation for the cohomology of the classifying space of the infinite unitary group. We also show that there is a unique Steenrod module structure on any unstable cyclic module that has dimension one in each complex degree (half the topological degree) with a fixed alpha-number (sum of “digits”) and is zero in other degrees.

Keywords

Steenrod algebra; unstable; Kudo-Araki-May algebra; complex projective space; BU

2010 Mathematics Subject Classification

55R40, 55R45, 55S05, 55S10

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