Čech-De Rham theory for leaf spaces of foliations

DOI10.1007/s00208-003-0473-2zbMath1043.57012arXivmath/0012069OpenAlexW2032939616MaRDI QIDQ1423608

Marius Crainic, Ieke Moerdijk

Publication date: 7 March 2004

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0012069

zbMATH Keywords

classifying spacecohomologyfoliationétale groupoidcharacteristic classes

Mathematics Subject Classification ID

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

Related Items (19)

Characterization of codimension one foliations on complex curves by connections ⋮ Chern-Weil map for principal bundles over groupoids ⋮ LOSIK CLASSES FOR CODIMENSION-ONE FOLIATIONS ⋮ The extension of cochain complexes of meromorphic functions to multiplications ⋮ Cosimplicial meromorphic functions cohomology on complex manifolds ⋮ Product-type classes for vertex algebra cohomology of foliations on complex curves ⋮ Smoothness of holonomy covers for singular foliations and essential isotropy ⋮ Atiyah sequences, connections and characteristic forms for principal bundles over groupoids and stacks ⋮ Noncommutative geometry of foliations ⋮ A Thom isomorphism in foliated de Rham theory ⋮ Hierarchies of holonomy groupoids for foliated bundles ⋮ Foliation groupoids and their cyclic homology ⋮ Index theory and non-commutative geometry. I: Higher families index theory ⋮ The holonomy groupoids of singularly foliated bundles ⋮ A characteristic map for the holonomy groupoid of a foliation ⋮ Non-diffeomorphic Reeb foliations and modified Godbillon-Vey class ⋮ Compactly supported analytic indices for Lie groupoids ⋮ The Godbillon-Vey invariant and equivariant \(KK\)-theory ⋮ Representations of étale Lie groupoids and modules over Hopf algebroids

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