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

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.

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.

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     author = {Wallet, Guy},
     title = {Holonomie et cycle \'evanouissant},
     journal = {Annales de l'Institut Fourier},
     pages = {181--186},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {31},
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     year = {1981},
     doi = {10.5802/aif.854},
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Wallet, Guy. Holonomie et cycle évanouissant. Annales de l'Institut Fourier, Tome 31 (1981) no. 4, pp. 181-186. doi : 10.5802/aif.854. http://www.numdam.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 | Zbl

[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 | Zbl

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

[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

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