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Mathematische Annalen

, Volume 328, Issue 1–2, pp 59–85 | Cite as

Čech-De Rham theory for leaf spaces of foliations

  • Marius Crainic
  • Ieke Moerdijk
Article

Abstract

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 version of Poincare duality for foliations.

Keywords

foliations characteristic classes étale groupoids classifying spaces cohomology 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Marius Crainic
    • 1
  • Ieke Moerdijk
    • 1
  1. 1.Department of MathematicsUtrecht UniversityThe Netherlands

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