Abstract
Let ( Y, X) be a relative CW complex with X and Y simply-connected and suppose that the relative homology H ∗(Y, X; k) is nonzero. Denote by F the homotopy fibre of the inclusion X → Y. We show that the grade of H ∗(F;k) as a module over H ∗(ΩY;k) is less than the relative cone length cl( Y, X). This result appears as a corollary of a deeper result concerning differential modules over differential graded algebras.
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