Hurewicz images of real bordism theory and real Johnson–Wilson theories

Abstract

We show that the Hopf elements, the Kervaire classes, and the κ¯-family in the stable homotopy groups of spheres are detected by the Hurewicz map from the sphere spectrum to the C2-fixed points of the Real bordism spectrum. A subset of these families is detected by the C2-fixed points of Real Johnson–Wilson theory ER(n), depending on n. In the proof, we establish an isomorphism between the slice spectral sequence and the C2-equivariant May spectral sequence of BPR.