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

  1. Jul 7, 2012 #1

    lavinia

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    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.
     
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  3. Jul 7, 2012 #2

    quasar987

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

    Isn't this done in Milnor Stacheff ?!?
     
  4. Jul 8, 2012 #3

    lavinia

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

    No. I think just the Z2 cohomology. I will check again.
     
  5. Jul 9, 2012 #4

    Bacle2

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

    Don't you use classifying spaces for this?
     
  6. Jul 9, 2012 #5

    lavinia

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    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.
     
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