%0 Journal Article
%T De Rham cohomology of diffeological spaces and foliations
%A G. Hector
%A E. Mac¨ªas-Virg¨®s
%A E. Sanmart¨ªn-Carb¨®n
%J Mathematics
%D 2009
%I arXiv
%X Let $(M,\mathcal{F})$ be a foliated manifold. We prove that there is a canonical isomorphism between the complex of base-like forms $\Omega^*_b(M,\mathcal{F})$ of the foliation and the "De Rham complex" of the space of leaves $M/\mathcal{F}$ when considered as a "diffeological" quotient. Consequently, the two corresponding cohomology groups $H^*_b(M,\mathcal{F})$ and $H^*(M/\mathcal{F})$ are isomorphic.
%U http://arxiv.org/abs/0903.2871v1