Abstract
We show, in contrast to the cases of complex and quaternionic partial flag manifolds, the rational cohomology rings of the real and oriented partial flag manifolds are generated not only by the characteristic classes of their canonical vector bundles, but also by exterior algebras arising from the rational cohomology rings of real Stiefel manifolds. We also discuss the rational and the mod-2 equivariant cohomology rings of these partial flag manifolds for certain canonical actions of tori and 2-tori.
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