The ER(n)-cohomology of BO(q) and real Johnson–Wilson orientations for vector bundles

kitchloo, nitu; wilson, w. stephen;

Using the Bockstein spectral sequence developed previously by the authors, we compute the ring ER(n)∗(BO(q)) explicitly. We then use this calculation to show that the ring spectrum MO[2n+1] is ER(n)-orientable (but not ER(n + 1)-orientable), where MO[2n+1] is defined as the Thom spectrum for the self-map of BO given by multiplication by 2n+1.