Differential graded modules over a nonconnected differential graded algebra

AbstractLet Λ∗ be a not necessarily connected differential graded algebra. To each Λ∗-differential graded module we associate ‘characteristic’ classes which are invariants of the quasi-isomorphism class of this module and determine the Pontrjagin product by the 0th and the first homology group of Λ∗. We use them to determine the differential d2 of homology spectral sequences such as the Serre spectral sequence or the Borel equivariant spectral sequence. This is done without classical hypothesis such as a one-connected base or a connected group