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arXiv · 0903.2871

De Rham cohomology of diffeological spaces and foliations

G. Hector·E. Macías-Virgós·E. Sanmartín-Carbón
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Abstract

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.

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G. Hector, E. Macías-Virgós, E. Sanmartín-Carbón. 2009-03-16. De Rham cohomology of diffeological spaces and foliations. https://arxiv.org/abs/0903.2871

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