Brown-Peterson cohomology from Morava \(K\)-theory (Q1273636)

This paper gives the structure of the Brown-Peterson cohomology of a wide class of spaces -- those with Morava \(K\)-theory concentrated in even dimensions. These spaces include: Eilenberg-Maclane spaces, loop spaces of finite Postnikov systems, and classifying spaces of most finite groups whose Morava \(K\)-theory is known. The main result is that for such spaces the Brown-Peterson cohomology is also concentrated in even dimensions and is flat as a \(BP^{*}\)-module for the category of finitely presented \(BP^{*}(BP)\)-modules. The proofs rely heavily on computations with the Atiyah-Hirzebruch spectral sequence.