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I am considering the restriction homomorphism $H^p(G_n(\mathbb{R}^\infty)) \leftarrow H^p(G_n(\mathbb{R}^{n+k}))$, where the $G_n(-)$ are the relevant Grassman manifolds. Does anyone know of conditions on $p,k$ which ensure that this map is in fact an isomorphism?

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Have you checked Milnor-Stasheff? I think $p < k$ should suffice –  Juan S Apr 26 '12 at 0:26

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