Norms of Eilenberg-Mac Lane Spectra and Real Bordism

Abstract

We provide a new method to compute the (homotopy) fixed-points of the permutation action on HF2∧HF2 by relating it to Real bordism. More precisely, we identify the C4-pullback of the C2-spectrum NC2eHF2 with a localization of NC4C2MUR. This allows us to use the localized slice spectral sequence for the computation of πC2★NC2eHF2. From this, we compute the first eight homotopy groups and deduce an infinite family of differentials in the homotopy fixed point spectral sequence.