what is the integer cohomology of the real infinite dimensional Grassmann manifold?

lavinia

I can't seem to find on the web a site that gives the Z cohomology of the infinite dimensional Grassmann manifold of real unoriented k planes in Euclidean space.

I am interested in computing the Bockstein exact sequence for the coefficient sequence,

0 -> Z ->Z ->Z/2Z -> 0

to see which products of the Stiefel-Whitney classes are mod 2 reductions of integer classes.

quasar987

Isn't this done in Milnor Stacheff ?!?

lavinia

No. I think just the Z2 cohomology. I will check again.

Bacle2

Don't you use classifying spaces for this?

lavinia

yes but for the Grassmann of unoriented planes I can only find the Z2 cohomology.