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 C 2 -fixed points of the Real bordism spectrum. A subset of these families is detected by the C 2 -fixed points of Real Johnson–Wilson theory E R (n) , depending on n. In the proof, we establish an isomorphism between the slice spectral sequence and the C 2 -equivariant May spectral sequence of B P R. [ABSTRACT FROM AUTHOR]