The Brown-Peterson cohomology of the classifying spaces of the projective unitary groups 𝑃𝑈(𝑝) and exceptional Lie groups

Abstract

For a fixed prime p p , we compute the Brown-Peterson cohomologies of classifying spaces of P U ( p ) PU(p) and exceptional Lie groups by using the Adams spectral sequence. In particular, we see that B P ∗ ( B P U ( p ) ) BP^*(BPU(p)) and K ( n ) ∗ ( B P U ( p ) ) K(n)^*(BPU(p)) are even dimensionally generated.