# Čech-De Rham theory for leaf spaces of foliations

@article{Crainic2000echDeRT, title={{\vC}ech-De Rham theory for leaf spaces of foliations}, author={Marius Crainic and Ieke Moerdijk}, journal={Mathematische Annalen}, year={2000}, volume={328}, pages={59-85} }

We present a new ‘‘Čech-De Rham’’ model for the cohomology of the classifying space of a foliated manifold. This model enables us to lift the construction of known characteristic classes in the cohomology of the manifold to the cohomology of the classifying space, by standard geometric methods and without making any reference to (necessarily non-Hausdorff) groupoids and their classifying spaces. We also show how the Čech-De Rham model can be used to prove some other known formulas, as well as a…

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