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An extension of the Reeb stability theorem. (English) Zbl 0860.57022

The author gives a generalization of the Reeb stability theorem. This generalization includes the Haefliger and the Thurston generalizations as special cases.

MSC:

57R30 Foliations in differential topology; geometric theory
22A22 Topological groupoids (including differentiable and Lie groupoids)
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[1] Bott, R., Characteristic classes and foliations, (Lecture Notes in Mathematics, 279 (1972), Springer: Springer Berlin), 1-94 · Zbl 0241.57010
[2] Brown, R., From groups to groupoids: a brief survey, Bull. London Math. Soc., 19, 113-134 (1987) · Zbl 0612.20032
[3] Camacho, C.; Neto, A., Geometric Theory of Foliations (1985), Birkhäuser: Birkhäuser Boston · Zbl 0568.57002
[4] Connes, A., A survey of foliations and operator algebras, (Operator Algebras and Applications. Operator Algebras and Applications, Proc. Sympos. Pure Math., 38 (1982)), 521-628, Part I · Zbl 0531.57023
[5] Connes, A., Non-commutative differential geometry, Publ. Math. IHES, 62, 41-144 (1985) · Zbl 0592.46056
[6] Ehresmann, C., Sur les espaces localement homogènes, Enseign. Math., 35, 317-333 (1936)
[7] van Est, W. T., Rapport sur les \(S\)-atlas, Astérisque, 116, 235-292 (1984) · Zbl 0543.58003
[8] Haefliger, A., Structures feuilletées et cohomologie à valeur dans un faisceau de groupoïdes, Comment. Math. Helv., 32, 248-329 (1958) · Zbl 0085.17303
[9] Hilsum, M.; Skandalis, G., Morphismes \(K\)-orientes d’espaces de feuilles et functorialite en theorie de Kasparov, Ann. Sci. École Norm. Sup., 20, 325-390 (1987) · Zbl 0656.57015
[10] Kuiper, N. H., Sur les surfaces localement affines, (Géométrie Différentielle, Colloques Internationaux du Centre National de la Recherche Scietifique. Géométrie Différentielle, Colloques Internationaux du Centre National de la Recherche Scietifique, Strasbourg (1953)), 79-87 · Zbl 0053.13003
[11] Lang, S., Differential Manifolds (1972), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0239.58001
[12] Moerdijk, I., Classifying toposes and foliations, Ann. Inst. Fourier (Grenoble), 41, 189-209 (1991) · Zbl 0727.57029
[13] Moerdijk, I., The classifying topos of a continuous groupoid I, Trans. Amer. Math. Soc., 310, 629-668 (1988) · Zbl 0706.18007
[14] Moerdijk, I., Toposes and groupoids, (Lecture Notes in Mathematics, 1348 (1988), Springer: Springer Berlin), 280-298 · Zbl 0659.18008
[15] Molino, P., Riemannian Foliations (1988), Birkhäuser: Birkhäuser Boston · Zbl 0633.53001
[16] Reeb, G., Sur Certaines Propriétés Topologiques des Variétés Feuilletées, (Actualités Scientifiques et Industrielles, 1183 (1952), Hermann: Hermann Paris) · Zbl 0049.12602
[17] Reeb, G.; Schweitzer, P., Un theoreme de Thurston etabli au moyen de l’analyse non standard, (Lecture Notes in Math., 652 (1978)), 138 · Zbl 0405.58011
[18] Schachermayer, W., Une modification standard de la demonstration non standard de Reeb at Schweitzer, (Lecture Notes in Math., 652 (1978)), 139-140 · Zbl 0405.58012
[19] Thurston, W. P., A generalization of the Reeb stability theorem, Topology, 13, 347-352 (1974) · Zbl 0305.57025
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