SPACES WITH POLYNOMIAL MOD-P COHOMOLOGY
Dietrich Notbohm
In the early seventieth, 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 \prg\ 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
and, for odd primes, answer Steenrod's question completely.
e-mail: notbohm at cfgauss.uni-math.gwdg.de