par Bertelson, Mélanie
Référence Pacific journal of mathematics, 252, 2, page (257-274)
Publication Publié, 2011
Article révisé par les pairs
Résumé : The validity of the Künneth formula for foliated cohomology, that is, for the tangential de Rham cohomology of a foliated manifold, is investigated. The main difficulty encountered is the non-Hausdorff nature of the foliated cohomology spaces, forbidding the completion of the tensor product. We present versions of the Künneth formula when both factors have Hausdorff foliated cohomology and when one factor has finite-dimensional foliated cohomology and a compact underlying manifold. We also give a counterexample to an alternative version of the Künneth formula. The proof of the second result involves a right inverse for the foliated de Rham differential. © 2011 by Pacific Journal of Mathematics.