Subject: A question on cohomology and homology of some homogeneous spaces From: Dmitry Kerner Date: Fri, 25 Feb 2005 05:08:05 -0800 (PST) Dear topologists, I have a question on the cohomology ring and representatives of homology classes of the following spaces. Consider the space of (complex, nonzero) $k\times n$ matrices (projectivised, i.e. taken up to multiplication by scalar matrix). The group O(k) (or U(k)) acts on this space (by multiplication from the left). Factor by the action of this group. Where can I find (any information) about cohomology ring of this space, the explicit representatives of homology classes etc. The same question, if instead of O(k) (U(k)) we factor by a group of k by k (nonzero) matrices with left lower block (of dimension $r \times k-r$) consisting of zeros only. Any references or hints on explicit solution are welcome.