Smoothability of proper foliations
Cantwell, John ; Conlon, Lawrence
Annales de l'Institut Fourier, Tome 38 (1988), p. 219-244 / Harvested from Numdam
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Il a été prouvé que toutes les variétés feuilletées compactes de classe C 2 , de codimension 1, dont toutes les feuilles sont propres, sont de classe C ∞ . Plus précisément, une telle variété feuilletée est homéomorphe à une variété de classe C ∞ . En d’autres termes, le résultat n’est pas vrai pour un feuilletage à feuilles non-propres. Dans ce cas précis, il y a une différence du point de vue topologique entre les classes C r et C r+1 , pour tout entier naturel r.

Compact, C 2 -foliated manifolds of codimension one, having all leaves proper, are shown to be C ∞ -smoothable. More precisely, such a foliated manifold is homeomorphic to one of class C ∞ . The corresponding statement is false for foliations with nonproper leaves. In that case, there are topological distinctions between smoothness of class C r and of class C r+1 for every nonnegative integer r.

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     author = {Cantwell, John and Conlon, Lawrence},
     title = {Smoothability of proper foliations},
     journal = {Annales de l'Institut Fourier},
     volume = {38},
     year = {1988},
     pages = {219-244},
     doi = {10.5802/aif.1146},
     mrnumber = {90f:57034},
     zbl = {0644.57013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1988__38_3_219_0}
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Cantwell, John; Conlon, Lawrence. Smoothability of proper foliations. Annales de l'Institut Fourier, Tome 38 (1988) pp. 219-244. doi : 10.5802/aif.1146. http://gdmltest.u-ga.fr/item/AIF_1988__38_3_219_0/

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