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

Abstract

The Steenrod algebra structures of H ∗ ( B G ; Z / p ) {H^\ast }(BG;Z/p) for compact Lie groups are studied. Using these, Brown-Peterson cohomology and Morava K 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 o d d ( B G ) = 0 B{P^{odd}}(BG) = 0 .