Talk:Grassmannian

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Mathematics rating:	Start Class	Mid Priority	Field: Geometry
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. History and general clean-up needed (consistent notation, wikify etc.). Geometry guy 14:33, 22 April 2007 (UTC)

[edit] Construction of a vector field

This argument that I wrote down for χG_n,k = χG_{n − 1,k − 1} + ( − 1)^kχG_{n − 1,k} it seems to imply that for all n and k, and χG_n,k = 0 if and only if n is even and k is odd. So G_6,3 has a non-vanishing vector field. Does anyone know how to construct such a vector field? Rybu 23:14, 8 April 2007 (UTC)

[edit] Schubert Cells

The explanations on the Schubert cell look a little bit confusing to me. I think they need to be more explicit. Unfortunately, I didn't find anything in the few math books I have. --Lhead 23:56, 15 May 2007 (UTC)

[edit] Orientation

I have a similar problem. Does anyone how to handle the orientation? If G(n,k) are the k-dimensional subspaces of R^n I learned that G(n,k) is orientable for n even and non-orientable for n odd. Does anyone know a prove for that. I managed to find one for the n even case which has a lot of computation in it and seems a bit unelegant. But the prove for the n odd case seems to be wrong in the source I have. I only know a method for proving that a manifold is non-orientable which uses vector fields that I am not able to handle too. Can anyone help or at least give a hint for some good sources about that? —Preceding unsigned comment added by Del the living manga (talk • contribs) 22:05, 15 October 2007 (UTC)