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Does the cohomology ring of a simply-connected space X determine the cohomology groups of ΩX?One could try to apply the Eilenberg-Moore spectral sequence to the pullback diagram • → X ← •, obtaining a spectral sequence TorH•(X, R)(R, R) => H•(ΩX, R), but could there be differentials or extension problems which differ for different spaces X with the same cohomology ring?
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