De Rham cohomology of diffeological spaces and foliations

Details De Rham cohomology of diffeological spaces and foliations De Rham cohomology of diffeological spaces and foliations

2009-03-16

arxiv.org/abs/0903.2871v1

Mathematics

Differential Geometry

13 pages

Scientific paper

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.

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