Holonomie et cycle évanouissant
Annales de l'Institut Fourier, Volume 31 (1981) no. 4, pp. 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.

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     title = {Holonomie et cycle \'evanouissant},
     journal = {Annales de l'Institut Fourier},
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Wallet, Guy. Holonomie et cycle évanouissant. Annales de l'Institut Fourier, Volume 31 (1981) no. 4, pp. 181-186. doi : 10.5802/aif.854. https://aif.centre-mersenne.org/articles/10.5802/aif.854/

[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

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