D. W. Kahn defined a spectral
sequence 𝒞(X;R) for the Postnikov system 𝒫(X) of a 1-connected CW-complex
which converges to H∗(X;R), the singular homology of X with coefficients in R. We
study 𝒞(X;R) in two settings: (a) to give a generalization of the classical theorem of
Eilenberg and MacLane concerning the dependence of Hi(X;Z) on the first
nonzero homotopy group of X(2.1) and (b) to give a complete computation of
Hi(X;Q)(Q = rationals) for i ≦ 3 ⋅c(X) ( c(X) = connectivity of X) in terms of the
graded homotopy group Π ⊗ Q = {πi(X) ⊗ Q∣0 < i ≦ 3 ⋅ c(X)} and the Whitehead
product on this group (0.1 and 0.2).
