Topological aspects of completely integrable foliations

Abstract

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.

References in corpus (1)

• Intermediate co-t-structures, two-term silting objects, tau-tilting modules, and torsion classes

Cited by in corpus (11)

• Classification of two-term tilting complexes over Brauer graph algebras
• Classifying tilting complexes over preprojective algebras of Dynkin type
• Silting objects
• Wide subcategories are semistable
• Discreteness of silting objects and t-structures in triangulated categories
• Contractible stability spaces and faithful braid group actions
• Derived categories of graded gentle one-cycle algebras
• Jordan-Hölder theorems for derived categories of derived discrete algebras
• Discrete triangulated categories
• The Ziegler spectrum for derived-discrete algebras
• Topological structure of spaces of stability conditions and topological Fukaya type categories