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

Cenkl , Bohumil ^[1] ; Richard Porter ^[1]
1. [1] Northeastern University
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 26, Nº 3, 1982, págs. 9-29
Idioma: inglés
DOI: 10.5565/publmat_26382_01
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Resumen
- 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.