Abstract
Let BG be the classifying space for stable spherical fibrations, and let V be a finite dimensional vector subspace of the cohomology algebra H ∗( BG; Z 2). We prove that V may be realized by a Poincaré duality space P, which means that if v: P→ BG is the Spivak fibration, then v ∗ maps V isomorphically onto its image in H ∗( P; Z 2). By construction, P is the product of a certain Grassman manifold and a spherical fiber space over a closed smooth manifold.
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