The fibre-cofibre construction and its applications

AbstractLet F→iE→pB be a fibration and let f: W→E be such that pf is homotopically trivial. Then p naturally extends to a fibration F′→i′E′→p′B with E′≅Cf the cone of f.In our first result, we study the natural homomorphism of H∗(ΩB;R)-modules H∗(F;R)→ H∗(F′;R). When R=Q, we apply this result to study the cone length of a space, the free Lie ideals and a cellular construction of a graded Lie algebra