Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Cohomology morphisms from $ H\sp *(B{\rm U};{\bf Z}/p)$ to $ H\sp *(B{\bf Z}/p;{\bf Z}/p)$

Author: Terrence Paul Bisson
Journal: Proc. Amer. Math. Soc. 101 (1987), 363-370
MSC: Primary 55S10; Secondary 55R35, 55R40
MathSciNet review: 902557
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Abstract: In this paper we use Hopf algebra and generating function methods to determine the group of all cohomology morphisms from $ {H^ * }\left( {BU;Z/p} \right)$ to $ {H^ * }\left( {BZ/p;Z/p} \right)$ that preserve the Steenrod operations, where $ p$ is an odd prime. The group $ \left[ {BZ/p,BU} \right]$ of homotopy classes of maps from $ BZ/p$ to BU, which can be calculated directly, is seen to be naturally isomorphic to the group of cohomology morphisms. For $ BZ/2$ and BO with coefficients in $ Z/2$ there are precisely similar results.

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Keywords: Classifying spaces, Steenrod operations, generating functions, $ p$-adic numbers
Article copyright: © Copyright 1987 American Mathematical Society