Compact, -foliated manifolds of codimension one, having all leaves proper, are shown to be -smoothable. More precisely, such a foliated manifold is homeomorphic to one of class . The corresponding statement is false for foliations with nonproper leaves. In that case, there are topological distinctions between smoothness of class and of class for every nonnegative integer .
Il a été prouvé que toutes les variétés feuilletées compactes de classe , de codimension 1, dont toutes les feuilles sont propres, sont de classe . Plus précisément, une telle variété feuilletée est homéomorphe à une variété de classe . 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 et , pour tout entier naturel .
@article{AIF_1988__38_3_219_0, author = {Cantwell, John and Conlon, Lawrence}, title = {Smoothability of proper foliations}, journal = {Annales de l'Institut Fourier}, pages = {219--244}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {38}, number = {3}, year = {1988}, doi = {10.5802/aif.1146}, mrnumber = {90f:57034}, zbl = {0644.57013}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1146/} }
TY - JOUR AU - Cantwell, John AU - Conlon, Lawrence TI - Smoothability of proper foliations JO - Annales de l'Institut Fourier PY - 1988 SP - 219 EP - 244 VL - 38 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1146/ DO - 10.5802/aif.1146 LA - en ID - AIF_1988__38_3_219_0 ER -
Cantwell, John; Conlon, Lawrence. Smoothability of proper foliations. Annales de l'Institut Fourier, Volume 38 (1988) no. 3, pp. 219-244. doi : 10.5802/aif.1146. http://www.numdam.org/articles/10.5802/aif.1146/
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