Smoothability of proper foliations
Annales de l'Institut Fourier, Tome 38 (1988) no. 3, pp. 219-244.

Il a été prouvé que toutes les variétés feuilletées compactes de classe C2, 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 Cr et Cr+1, pour tout entier naturel r.

Compact, C2-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 Cr and of class Cr+1 for every nonnegative integer r.

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     title = {Smoothability of proper foliations},
     journal = {Annales de l'Institut Fourier},
     pages = {219--244},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {38},
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     year = {1988},
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Cantwell, John; Conlon, Lawrence. Smoothability of proper foliations. Annales de l'Institut Fourier, Tome 38 (1988) no. 3, pp. 219-244. doi : 10.5802/aif.1146. https://www.numdam.org/articles/10.5802/aif.1146/

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