Chapter V the Homotopy Groups of H Ring Spectra

This section contains statements of our results on homotopy operations as well as some applications of these results. The proofs depend on material in §2 and will be given in §3Note that, aside from the computations in ~,S at the end of this section, all the results here apply to the homotopy of any H ring spectrum Y. Let ~:DpY + Y denote the structure map. The order of results in this section is: relation to other operations, particular operations and relations, Cartan formulas, computations in w,S, remarks. In order not to interrupt the main flow of ideas, we have deferred a number of remarks until the end of the section. Throughout this section let Er(X,Y) be the ordinary mod p Adams spectral sequence converging to IX,Y]., and let Er(S,~ ) be the spectral sequence of IV §6 based on ordinary rood p homology. Let ~ be the sequence