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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