Let n <= m and G:=Gr(n,m) be the (real) Grassmanian manifold. I understand the topology of the simplest case, that of projective space, and am wondering if there is a way to interpret the topology of the G to similar to projective space, with the according generalizations needed.(adsbygoogle = window.adsbygoogle || []).push({});

If V^n is an element (vector subspace) of G, then how can I picture a neighborhood of it? The book I have is crap, has no proofs and the author (some Harvard guy) is basically writing for people who know this sh!t already, so in my opinion it defeats the purpose. But back to the question, can anyone help me out here in understand the topology of the Grassmanian, or point me to a good reasonable source where I can read this in?

Thanks in advance!

CM

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# The Grassmanian manifold's topology

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