CechDe Rham theory for leaf spaces of foliations
Abstract
The purpose of this paper is to present a ``CechDe Rham'' model for the cohomology of leaf spaces. This model lends itself to the construction of characteristic classes (in the cohomology of classifying spaces) by explicit geometrical constructions which are immediate extensions of the standard constructions for manifolds. In particular we rediscover (and explain) the Thurston formula and the Bott formulas for cocycles on diffeomorphism groups. We also use the CechDe Rham model to explicitly describe the relation between the cohomology of the classifying space, the basic cohomology, and the foliated cohomology of foliations.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2000
 arXiv:
 arXiv:math/0012069
 Bibcode:
 2000math.....12069C
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Algebraic Topology;
 Mathematics  Dynamical Systems;
 Mathematics  KTheory and Homology
 EPrint:
 22 pages