Integer Cohomology of 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]

Isn't this done in Milnor Stacheff ?!?

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

 

[Bacle2]

Don't you use classifying spaces for this?

 

[lavinia]

Don't you use classifying spaces for this?

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