De Rham cohomology of diffeological spaces and foliations

Hector, G.; Macías-Virgós, E.; Sanmartín-Carbón, E.

De Rham cohomology of diffeological spaces and foliations

Authors

Hector, G.

Macías-Virgós, E.

Sanmartín-Carbón, E.

Description

Let $(M,\mathcal{F})$ be a foliated manifold. We prove that there is a canonical isomorphism between the complex of base-like forms $Ω^*_b(M,\mathcal{F})$ 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.
13 pages