{"paper":{"title":"Godbillon-Vey sequence and Francoise algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dmitry Novikov, Jessie Pontigo-Herrera, Laura Ortiz-Bobadilla, Pavao Mardesic","submitted_at":"2019-01-26T19:36:53Z","abstract_excerpt":"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 $\\gamma(t)\\subset F^{-1}(t)$.\n  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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09268","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}