Cohomology of diffeological spaces and foliations

Details Cohomology of diffeological spaces and foliations Cohomology of diffeological spaces and foliations

2007-06-15

arxiv.org/abs/0706.2313v1

Mathematics

Differential Geometry

6 pages

Scientific paper

Let (M,F) be a foliated manifold. We study the relationship between the basic
cohomology Hb(M,F) of the foliation and the De Rham cohomology H(DF) of the
space of leaves M/F as a quotient diffeological space. We prove that for an
arbitrary foliation there is a morphism from H(DF) to Hb(M,F). It is an
isomorphism when F is a Q-foliation.

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