Godbillon–Vey sequence and Françoise algorithm

Abstract : We consider foliations given by deformations of exact forms dF in in a neighborhood of a family of cycles . In 1996 Françoise gave an algorithm for calculating the first nonzero term of the displacement function Δ along γ of such deformations. This algorithm recalls the well-known Godbillon–Vey sequences discovered in 1971 for investigation of integrability of a form ω. In this paper, we establish the correspondence between the two approaches and translate some results by Casale relating types of integrability for finite Godbillon–Vey sequences to the Françoise algorithm settings. Previous article Next article MSC primary34C07 34M15 34C05 secondary34C08
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02094588
Contributeur : Imb - Université de Bourgogne <>
Soumis le : mardi 9 avril 2019 - 17:18:41
Dernière modification le : jeudi 4 juillet 2019 - 13:41:57

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Pavao Mardešić, Dmitry Novikov, Laura Ortiz-Bobadilla, Jessie Pontigo-Herrera. Godbillon–Vey sequence and Françoise algorithm. Bulletin des Sciences Mathématiques, Elsevier, 2019, 153, pp.72-85. ⟨https://doi.org/10.1016/j.bulsci.2019.02.001⟩. ⟨10.1016/j.bulsci.2019.02.001⟩. ⟨hal-02094588⟩

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