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Čech-De Rham theory for leaf spaces of foliations

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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.

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Authors and Affiliations

  1. Department of Mathematics, Utrecht University, PO Box 800 10, 3508, TA, Utrecht, The Netherlands

    Marius Crainic & Ieke Moerdijk

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  1. Marius Crainic
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  2. Ieke Moerdijk
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Mathematics Subject Classification (2000):57D30, 57R32, 22A22, 55R40, 57D20

Research supported by NWO

Received: 8 November 2001

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Crainic, M., Moerdijk, I. Čech-De Rham theory for leaf spaces of foliations. Math. Ann. 328, 59–85 (2004). https://doi.org/10.1007/s00208-003-0473-2

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