Holonomie et cycle évanouissant
Annales de l'Institut Fourier, Volume 31 (1981) no. 4, p. 181-186

We prove that the holonomy is not trivial in a neighbourhood of a vanishing cycle using a theorem of Imanishi and we also give a proof of this theorem by the help of non-standard methods.

On démontre que l’holonomie est non triviale au voisinage d’un cycle évanouissant au moyen d’un critère d’Imanishi et on donne une démonstration non standard de ce dernier.

@article{AIF_1981__31_4_181_0,
     author = {Wallet, Guy},
     title = {Holonomie et cycle \'evanouissant},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {31},
     number = {4},
     year = {1981},
     pages = {181-186},
     doi = {10.5802/aif.854},
     zbl = {0469.57020},
     mrnumber = {83c:57013},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1981__31_4_181_0}
}
Wallet, Guy. Holonomie et cycle évanouissant. Annales de l'Institut Fourier, Volume 31 (1981) no. 4, pp. 181-186. doi : 10.5802/aif.854. http://www.numdam.org/item/AIF_1981__31_4_181_0/

[1] H. Imanishi, On the Theorem of Denjoy-Sacksteder for Codimension One Foliations without Holonomy, J. Math. Kyoto Univ., 14-3 (1974), 607-634. | MR 51 #4270 | Zbl 0296.57006

[2] E. Nelson, Internal Set Theory : a New Approach to Nonstandard Analysis, Bull. of the Amer. Math. Soc., vol. 83, n° 6 (novembre 1977). | MR 57 #9544 | Zbl 0373.02040

[3] R. Sacksteder, Foliations and Pseudo-groups, Amer. J. Math., 87 (1965), 79-102. | MR 30 #4268 | Zbl 0136.20903

[4] P. A. Schweitzer, Some Problems in Foliation Theory and Related Areas. Differential Topology, Foliations and Gelfand-Fuks Cohomology, Proceedings, Rio de Janeiro 1976, Lecture Notes in Mathematics, 652. | Zbl 0377.57001