On the Homology of Postnikov Fibers

Félix, Yves;Thomas, JC.
(1993) Proceedings of the American Mathematical Society — Vol. 118, n° 1, p. 255-258 (1993)

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  • Félix, YvesUCLouvain
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  • Thomas, JC.
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Abstract
Let k be a field of positive characteristic and X be a simply connected space of the homotopy type of a finite type CW complex. The Postnikov fibre X([n]) of X is defined as the homotopy fibre of the n-equivalence fn: X --> X(n) coming from the Postnikov tower {X(n)} of X. We prove that if the Lusternik-Schnirelmann category of X is finite, then H*(X[n];k) contains a free module on a subalgebra K of H* (OMEGAX(n);k) such that H* (OMEGAX(n);k) is a finite-dimensional free K-module.
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Félix, Y., & Thomas, JC. (1993). On the Homology of Postnikov Fibers. Proceedings of the American Mathematical Society, 118(1), 255-258. https://doi.org/10.2307/2160035 (Original work published 1993)