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arXiv · 1901.09268

Godbillon-Vey sequence and Francoise algorithm

Pavao Mardesic·Dmitry Novikov·Laura Ortiz-Bobadilla·Jessie Pontigo-Herrera
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Abstract

We consider foliations given by deformations $dF+\epsilon\omega$ of exact forms $dF$ in $\mathbb{C}^2$ in a neighborhood of a family of cycles $\gamma(t)\subset F^{-1}(t)$. In 1996 Francoise gave an algorithm for calculating the first nonzero term of the displacement function $\Delta$ along $\gamma$ of such deformations. This algorithm recalls the well-known Godbillon-Vey sequences discovered in 1971 for investigation integrability of a form $\omega$. 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 Francoise algorithm settings.

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Pavao Mardesic, Dmitry Novikov, Laura Ortiz-Bobadilla, Jessie Pontigo-Herrera. 2019-01-26. Godbillon-Vey sequence and Francoise algorithm. https://arxiv.org/abs/1901.09268

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