Vol. 40, No. 1, 1972

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ISSN: 0030-8730
Rational homology and Whitehead products

Micheal Neal Dyer

Vol. 40 (1972), No. 1, 59–71
Abstract

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) Q0 < i 3 c(X)} and the Whitehead product on this group (0.1 and 0.2).

Mathematical Subject Classification
Primary: 55H05
Milestones
Received: 5 October 1970
Revised: 7 June 1971
Published: 1 January 1972
Authors
Micheal Neal Dyer