Abstract
Etale groupoids play a central role in the theory of foliations. Well-known examples include the Haefliger groupoid Γq 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).
To P. Molino, on the occasion of his 6th birthday
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References
R. Bott, Characteristic classes and foliations, in Springer LNM 279 (1972), 1–94.
A.K. Bousfield, D.M. Kan, Homotopy Limits, Completions and Localizations, Springer LNM 304, 1972.
J.-L. Brylinski, V. Nistor, Cyclic cohomology of étale groupoids, K-Theory 8 (1994), 341–365.
A. Connes, Non Commutative Geometry, Academic Press, 1994.
W.T. van Est, Rapport sur les S-atlas, Astérisque 116 (1984), 235–292.
A. Haefliger, Homotopy and integrability, in: Springer LNM 197(1971), 133–163.
A. Haefliger, Differentiate Cohomology, CIME, Varenna, 1976.
A. Haefliger, Groupoïdes d’holonomie et classifiants, Astérisque 116 (1984), 70–97.
A. Haefliger, Cohomology theory for étale topological groupoids, unpublished manuscript, 1992.
S. Mac Lane, Categories for The Working Mathematician, Springer-Verlag, 1971.
I. Moerdijk, Classifying spaces and foliations, Ann. Inst. Fourier 41 (1991), 189–209.
I. Moerdijk, Classifying Spaces and Classifying Topoi, Springer LNM 1616 (1995).
I. Moerdijk, D.A. Pronk, Orbifolds, sheaves and groupoids, K-Theory (to appear).
P. Molino, Riemannian Foliations, Birkhäuser, 1988.
G.B. Segal, Classifying spaces and spectral sequences, Publ. Math. IHES 34 (1968), 105–112.
G.B. Segal, Categories and cohomology theories, Topology 13 (1974), 293–312.
G.B. Segal, Classifying spaces related to foliations, Topology 17 (1978), 367–382.
M. Artin, A. Grothendieck, J.-L. Verdier, Théorie de topos et cohomologie étale des schémas, tome 2, Springer LNM 270, (1972).
H. Winkelnkemper, The graph of a foliation, Ann. Global Anal. Geom. 1 (1983), 51–75.
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Moerdijk, I. (1997). On the Weak Homotopy Type of Étale Groupoids. In: Albert, C., Brouzet, R., Dufour, J.P. (eds) Integrable Systems and Foliations. Progress in Mathematics, vol 145. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4134-8_8
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DOI: https://doi.org/10.1007/978-1-4612-4134-8_8
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