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# 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: https://dx.doi.org/10.4310/HHA.2007.v9.n2.a13

#### Authors

#### 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

Published 1 January 2007