On fibrations related to real spectra

Abstract

We consider real spectra, collections of Z/(2)-spaces indexed over Z oplus Z alpha with compatibility conditions. We produce fibrations connecting the homotopy fixed points and the spaces in these spectra. We also evaluate the map which is the analogue of the forgetful functor from complex to reals composed with complexification. Our first fibration is used to connect the real 2^{n+2}(2^n-1)-periodic Johnson--Wilson spectrum ER(n) to the usual 2(2^n-1)-periodic Johnson--Wilson spectrum, E(n). Our main result is the fibration Sigma^{lambda(n)} ER(n) --> ER(n) --> E(n)$, where lambda(n) = 2^{2n+1}-2^{n+2}+1.