Resumen de Cup-i product and higher homotopies in the de rham complex

Bohumil Cenkl, Richard Porter

• In this note we give a description of the Steenrod squares starting with the analogue of the cup-i product in the deRhamcomplex of Cartan-Miller. The integration of forms over simplices, which induces the isomorphism on cohomology in the deRham theorem, is not an algebra map. It is proved that it induces a morphism of coalgebras . Therefore the cohomology of a pullback fibration can be computed in terms of the deRham complex in some cases.