An explicit classification of three-stage Postnikov towers (Q850851)

The author introduced a certain classifying space \(M_\infty\) in [Contemp. Math. 274, 79--104 (2001; Zbl 1033.55009)]. A based map \(B \rightarrow M_\infty\) determines a fibration over \(B\) whose fibers are products \(K(G, m) \times K(H, n)\) of two Eilenberg-Mac Lane spaces. The group of homotopy classes of based self-homotopy equivalences of a fiber acts on the set of pointed homotopy classes of maps from \(B\) to \(M_\infty\) and the orbit set classifies fibrations over \(B\) with fiber \(K(G, m) \times K(H, n)\), up to fibrewise homotopy. Simplifications in the stable range are discussed.