Postnikov extensions of ring spectra

!P2R! P1R! P0R! in the homotopy category of ring spectra. The levels come equipped with compatible maps R! PnR, and the n‐th level is characterized by having i.PnR/D 0 for i > n, together with the fact that i.R/! i.PnR/ is an isomorphism for i n. In this paper we produce k ‐invariants for the levels of this tower and explain their role in the following problem: if one only knows Pn 1R together with n.R/ as a 0.R/‐bimodule, what are the possibilities for PnR? Corollary 1.4 shows in what sense the possibilities are classified by k ‐invariants.

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