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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 suffice2012-04-26

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