Localization of Baum-Bott residues, generalized curves and \(K\)-theory. I. Foliations in \(\mathbb{C}^2\)

DOI10.1007/s00014-001-8324-9zbMath1003.32007OpenAlexW2092959060MaRDI QIDQ5956906

Daniel Lehmann, Vincent Cavalier

Publication date: 13 January 2003

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00014-001-8324-9

zbMATH Keywords

Baum-Bott residuessingular holomorphic foliationsK-theoryMilnor numbergeneralized curvesGoméz-Mont-Seade-Verjovsky indexPoincaré-Hopf index

Mathematics Subject Classification ID

Vector fields, frame fields in differential topology (57R25) Characteristic classes and numbers in differential topology (57R20) Singularities of holomorphic vector fields and foliations (32S65) Relations of (K)-theory with cohomology theories (19E20)

Related Items (5)

Chern classes for analytic sets. (Classes de Chern des ensembles analytiques) ⋮ Weierstrass 1-forms and nondicritical generalized curve foliations ⋮ Local polar invariants and the Poincaré problem in the dicritical case ⋮ Local polar invariants for plane singular foliations ⋮ Chern classes of analytic sets

Cites Work

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• The index of a holomorphic flow with an isolated singularity
• GENERALIZATION OF VARIATIONS AND BAUM–BOTT RESIDUES FOR HOLOMORPHIC FOLIATIONS ON SINGULAR VARIETIES
• Indices of Holomorphic Vector Fields Relative to Invariant Curves on Surfaces
• Reduction of Singularities of the Differential Equation Ady = Bdx

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