Vol. 62, No. 1, 1976

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Moore-Postnikov towers for fibrations in which π1(fiber) is non-abelian

Richard Oscar Hill

Vol. 62 (1976), No. 1, 141–148

When Moore-Postnikov towers for fibrations p : E X were first developed, Moore constructed the tower for arbitrary maps p and, when all action on πn (fiber) were trivial, showed that each stage was induced from the loop-path fibration over a K(π,n) and classified by the corresponding k-invariant. Barratt-Gugenheim-Moore showed that without restriction each stage could be induced from suitable universal fibrations. Subsequent authors, including McClendon, Nussbaum, Robinson and Siegal, based on the above and work by Olum, described the classifying map by k-invariant and local coefficients when π1(X) acts and π1 (fiber) is Abelian, and Bousfield and Kan described the case when π1 acts nilpotently. This note gives a method for handling fibrations requiring only that all spaces be path-connected.

Mathematical Subject Classification
Primary: 55G45, 55G45
Received: 18 February 1975
Published: 1 January 1976
Richard Oscar Hill