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Čech-De Rham theory for leaf spaces of foliations. (English) Zbl 1043.57012

A new Čech-de Rham model for the cohomology of the classifying space of a foliated manifold is presented. By this model, the construction of known characteristic classes in the cohomology of the manifold can be lifted to the cohomology of the classifying space by standard geometric methods. It is also used to prove some other known formulas, as well as a version of Poincaré duality for foliations.

MSC:

57R30 Foliations in differential topology; geometric theory
57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology
22A22 Topological groupoids (including differentiable and Lie groupoids)
55R40 Homology of classifying spaces and characteristic classes in algebraic topology
57R20 Characteristic classes and numbers in differential topology
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