Landweber flat real pairs and ER(n)-cohomology

Abstract

We take advantage of the internal algebraic structure of the Bockstein spectral sequence converging to ER(n)⁎(pt) to prove that for spaces Z that are part of Landweber flat real pairs with respect to E(n) (see Definition 2.9), the cohomology ring ER(n)⁎(Z) can be obtained from E(n)⁎(Z) by base change. In particular, our results allow us to compute the Real Johnson–Wilson cohomology of the Eilenberg–MacLane spaces Z=K(Z,2m+1),K(Z/2q,2m),K(Z/2,m) for any natural numbers m and q, as well as connective covers of BO: BO,BSO,BSpin and BO〈8〉.