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Spaces with polynomial mod-p cohomology

Published online by Cambridge University Press:  01 March 1999

D. NOTBOHM
Affiliation:
Mathematisches Institut, Bunssenstr. 3-5, 37073 Göttingen, Germany; e-mail: [email protected]

Abstract

In the early seventies, Steenrod posed the question: which polynomial algebras over the Steenrod algebra appear as the cohomology ring of a topological space? For odd primes, work of Adams and Wilkerson and Dwyer, Miller and Wilkerson showed that all such algebras are given as the mod-p reduction of the invariants of a pseudo reflection group acting on a polynomial algebra over the p-adic integers. We show that this necessary condition is also sufficient for finding a realization of such a polynomial algebra. We also show that, up to completion, every space with polynomial mod-p cohomology is equivalent to the product of the classifying space of a connected compact Lie group and some spaces determined by irreducible p-adic rational pseudo reflection groups.

Type
Research Article
Copyright
The Cambridge Philosophical Society 1999

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