# Topology and Geometry of Grassmannians $G_k(\mathbb{R}^n)$ or $G_k(\mathbb{C}^n)$ [closed]

What are the best books or (survey) articles ib the topology and geometry of Grassmannians $G_k(\mathbb{R}^n)$ or $G_k(\mathbb{C}^n)$. I am interested in:

• Is there a topological classification possible, using the extra structure of "being a Grassmannian" ?
• Is there a differential toppological classfificuation ? (for example: are there any exotic or fake Grassmannians) ?

This is the same question as http://math.stackexchange.com/questions/59414/books-on-topology-and-geometry-of-grassmannians. I have altered things a bit, since the stackexchange question is nuch to wide to ask here, I think.

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I don't understand -- you accepted an answer to the question there, so why post here? I will answer at MSE. –  Ryan Budney Aug 26 '11 at 7:25
I did not know this wasn't allowed. I don't know how many people are reading both blogs. I comment on your answer in stackexchange, yo keep all in one place. –  Willem Aug 26 '11 at 22:02