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

1. Jul 7, 2012

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.

2. Jul 7, 2012

quasar987

Re: what is the integer cohomology of the real infinite dimensional Grassmann manifol

Isn't this done in Milnor Stacheff ?!?

3. Jul 8, 2012

lavinia

Re: what is the integer cohomology of the real infinite dimensional Grassmann manifol

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

4. Jul 9, 2012

Bacle2

Re: what is the integer cohomology of the real infinite dimensional Grassmann manifol

Don't you use classifying spaces for this?

5. Jul 9, 2012

lavinia

Re: what is the integer cohomology of the real infinite dimensional Grassmann manifol

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