In the book To2, Totaro determined Chow rings CH∗(BG)/p of classifying spaces BG for all p-groups G of order |G|≤ p4. In this paper, we compute CH∗(BG)/2 for G = 2+1+4 = D8 · D8, which has nilpotent ...elements.
For a fixed prime p, we compute the Brown-Peterson cohomologies of classifying spaces of PU(p) and exceptional Lie groups by using \linebreak the Adams spectral sequence. In particular, we see that ...BP^*(BPU(p)) and K(n)^*(BPU(p)) are even dimensionally generated.
Let BG be the classifying space of a compact Lie group G. Some examples of computations of the motivic cohomology H^{*,*}(BG;\mathbb{Z}/p) are given, by comparing with H^*(BG;\mathbb{Z}/p), CH^*(BG) ...and BP^*(BG).
The BP^*-module structure of BP^*(BG) for extraspecial 2-groups is studied using transfer and Chern classes. These give rise to p-torsion elements in the kernel of the cycle map from the Chow ring to ...ordinary cohomology first obtained by Totaro.
In this paper we utilize BP*(), a generalized cohomology theory associated with the Brown-Peterson spectrum to prove a nonimmersion theorem for products of real projective spaces.
The Brown-Peterson cohomology rings of classifying spaces of finite groups are studied, considering relations to the other generalized cohomology theories. In particular, BP*(M) are computed for ...minimal nonabelian p-groups M. As an application, we give a necessary condition for the existence of nonabelian p-subgroups of compact Lie groups.
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