Topological aspects of completely integrable foliations

In this paper it is shown that the existence of two independent holomorphic first integrals for foliations by curves on (C^3,0) is not a topological invariant. More precisely, we provide an example of two topologically equivalent foliations such that only one of them admits two independent holomorph...

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Bibliographic Details
Published in:arXiv.org 2012-09
Main Authors: Pinheiro, Susana, Reis, Helena
Format: Article
Language:English
Subjects:
Integrals
Invariants
Mathematical analysis
Topology
Online Access:Get full text
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Summary:In this paper it is shown that the existence of two independent holomorphic first integrals for foliations by curves on (C^3,0) is not a topological invariant. More precisely, we provide an example of two topologically equivalent foliations such that only one of them admits two independent holomorphic first integrals. The existence of invariant surfaces over which the induced foliation possesses infinitely many separatrices possibly constitutes the sole obstruction for the topological invariance of complete integrability and a characterization of foliations admitting this type of invariant surfaces is also given.
ISSN:2331-8422
DOI:10.48550/arxiv.1209.2956