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Characteristic classes of finite group representations

  1. Aug 10, 2009 #1
    I know zero about the characteristic classes of finite group representations and would appreciate a reference.

    specifically, if I have a faithful representations of a finite group,G, in O(n) what can I say about the induced map on cohomology,

    P*:H*(BO(n))-> H*(BG) ?

    I am mostly interested in Z or Z/2 coefficients so this would be Pontryagin classes and Stiefel-Whitney classes.

    For instance what are the induced maps of these two representations of Z/2?

    -1 reflection of the real line

    -1 0
    0 -1 180 degree rotation of R^2.


    Can you show me an unoriented representation of the dihedral group of order 8 so that the induced map on Z/2 cohomology is not surjective?
     
    Last edited: Aug 10, 2009
  2. jcsd
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