Whitney regularity and generic wings
Annales de l'Institut Fourier, Volume 31 (1981) no. 2, p. 87-111
Given adjacent subanalytic strata (X,Y) in R n verifying Kuo’s ratio test (r) (resp. Verdier’s (w)-regularity) we find an open dense subset of the codimension k C 1 submanifolds W (wings) containing Y such that (XW,Y) is generically Whitney (b π )-regular is exactly one more than the dimension of the set of limits of vectors for which (b π ) fails. A general position argument for smooth strata is also given.
Étant donné un couple (X,Y) de strates sous-analytiques dans R n qui vérifient le critère (r) de Kuo (resp. la condition (w) de Verdier), nous trouvons un ouvert dense U des sous-variétés W de classe C 1 et codimension k qui contiennent Y (les ailes), telles que (XW,Y) vérifie (r)(resp.(w)) si WU. Si dimY=1, le plus petit entier k tel que (XW,Y) vérifie la condition (b π ) de Whitney est égal à 1+dimΛ π , où Λ π est l’ensemble des limites de vecteurs pour lesquels (b π ) n’est pas satisfaite. Grâce à un argument de position nous obtenons aussi un résultat pour les strates de classe C 1 .
@article{AIF_1981__31_2_87_0,
     author = {Aznar, V. Navarro and Trotman, David J. A.},
     title = {Whitney regularity and generic wings},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {31},
     number = {2},
     year = {1981},
     pages = {87-111},
     doi = {10.5802/aif.830},
     mrnumber = {82j:58009},
     zbl = {0442.58002},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_1981__31_2_87_0}
}
Whitney regularity and generic wings. Annales de l'Institut Fourier, Volume 31 (1981) no. 2, pp. 87-111. doi : 10.5802/aif.830. https://aif.centre-mersenne.org/item/AIF_1981__31_2_87_0/

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