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On the Weak Homotopy Type of Étale Groupoids

  • Ieke Moerdijk
Conference paper
Part of the Progress in Mathematics book series (PM, volume 145)

Abstract

Etale groupoids play a central role in the theory of foliations. Well-known examples include the Haefliger groupoid Γ q which classifies C -foliations of codimension q [H71] and the holonomy groupoid of any foliation [W83]. In particular, invariants of leaf spaces of foliations are usually defined in terms of the classifying space or the C*-algebra associated to this holonomy groupoid (see [C, H84, Mo, BN] and many others).

Keywords

Geometric Realization Riemannian Foliation Topological Category Local Homeomorphism Sheaf Cohomology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [B]
    R. Bott, Characteristic classes and foliations, in Springer LNM 279 (1972), 1–94.MathSciNetGoogle Scholar
  2. [BK]
    A.K. Bousfield, D.M. Kan, Homotopy Limits, Completions and Localizations, Springer LNM 304, 1972.Google Scholar
  3. [BN]
    J.-L. Brylinski, V. Nistor, Cyclic cohomology of étale groupoids, K-Theory 8 (1994), 341–365.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [C]
    A. Connes, Non Commutative Geometry, Academic Press, 1994.Google Scholar
  5. [vE]
    W.T. van Est, Rapport sur les S-atlas, Astérisque 116 (1984), 235–292.Google Scholar
  6. [H71]
    A. Haefliger, Homotopy and integrability, in: Springer LNM 197(1971), 133–163.MathSciNetGoogle Scholar
  7. [H76]
    A. Haefliger, Differentiate Cohomology, CIME, Varenna, 1976.Google Scholar
  8. [H84]
    A. Haefliger, Groupoïdes d’holonomie et classifiants, Astérisque 116 (1984), 70–97.MathSciNetGoogle Scholar
  9. [H92]
    A. Haefliger, Cohomology theory for étale topological groupoids, unpublished manuscript, 1992.Google Scholar
  10. [CWM]
    S. Mac Lane, Categories for The Working Mathematician, Springer-Verlag, 1971.zbMATHGoogle Scholar
  11. [M91]
    I. Moerdijk, Classifying spaces and foliations, Ann. Inst. Fourier 41 (1991), 189–209.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [M95]
    I. Moerdijk, Classifying Spaces and Classifying Topoi, Springer LNM 1616 (1995).Google Scholar
  13. [MP]
    I. Moerdijk, D.A. Pronk, Orbifolds, sheaves and groupoids, K-Theory (to appear).Google Scholar
  14. [Mo]
    P. Molino, Riemannian Foliations, Birkhäuser, 1988.zbMATHGoogle Scholar
  15. [S68]
    G.B. Segal, Classifying spaces and spectral sequences, Publ. Math. IHES 34 (1968), 105–112.zbMATHGoogle Scholar
  16. [S74]
    G.B. Segal, Categories and cohomology theories, Topology 13 (1974), 293–312.Google Scholar
  17. [S78]
    G.B. Segal, Classifying spaces related to foliations, Topology 17 (1978), 367–382.MathSciNetzbMATHCrossRefGoogle Scholar
  18. [SGA4]
    M. Artin, A. Grothendieck, J.-L. Verdier, Théorie de topos et cohomologie étale des schémas, tome 2, Springer LNM 270, (1972).Google Scholar
  19. [W83]
    H. Winkelnkemper, The graph of a foliation, Ann. Global Anal. Geom. 1 (1983), 51–75.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 1997

Authors and Affiliations

  • Ieke Moerdijk
    • 1
  1. 1.Department of MathematicsUtrecht UniversityUtrechtThe Netherlands

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