The Serre spectral sequence of a multiplicative fibration

Félix, Yves;Halperin, S.;Thomas, JC.
(2001) Transactions of the American mathematical society — Vol. 353, n° 9, p. 3803-3831 (2001)

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Authors
  • Félix, YvesUCLouvain
    Author
  • Halperin, S.
    Author
  • Thomas, JC.
    Author
Abstract
In a fibration OmegaF (Omegaj)under right arrow OmegaX (Omega pi )under right arrow OmegaB we show that finiteness conditions on F force the homology Serre spectral sequence with F-p-coefficients to collapse at some finite term. This in particular implies that as graded vector spaces, H-*(OmegaX) is "almost" isomorphic to H-*(OmegaB) circle times H-*(OmegaF). One consequence is the conclusion that X is elliptic if and only if B and F are.
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Félix, Y., Halperin, S., & Thomas, JC. (2001). The Serre spectral sequence of a multiplicative fibration. Transactions of the American mathematical society, 353(9), 3803-3831. https://doi.org/10.1090/S0002-9947-01-02801-X (Original work published 2001)