Brown-Peterson and ordinary cohomology theories of classifying spaces for compact Lie groups

Kono, Akira; Yagita, Nobuaki

doi:10.1090/S0002-9947-1993-1139493-4

Brown-Peterson and ordinary cohomology theories of classifying spaces for compact Lie groups
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by Akira Kono and Nobuaki Yagita PDF

Trans. Amer. Math. Soc. 339 (1993), 781-798 Request permission

Abstract:

The Steenrod algebra structures of ${H^\ast }(BG;Z/p)$ for compact Lie groups are studied. Using these, Brown-Peterson cohomology and Morava $K$-theory are computed for many concrete cases. All these cases have properties similar as torsion free Lie groups or finite groups, e.g., $B{P^{odd}}(BG) = 0$.

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