Euler obstruction, Brasselet number and critical points

We relate the Brasselet number of a complex analytic function-germ defined on a complex analytic set to the critical points of its real part on the regular locus of the link. Similarly we give a new characterization of the Euler obstruction in terms of the critical points on the regular part of the...

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Bibliographic Details
Published inResearch in the mathematical sciences Vol. 11; no. 2
Main Author Dutertre, Nicolas
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2024
Springer Nature B.V
Springer
Subjects
Analytic functions
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Critical point
Mathematics
Mathematics and Statistics
Critical points
14P10
Euler obstruction
57R70
Gauss–Bonnet curvature
32C18
14B05
Mathematics Subject Classification : 14B05
Mathematics Subject Classification : 14B05 14P10 32C18 57R70 Euler obstruction Gauss-Bonnet curvature critical points
Gauss-Bonnet curvature
57R70 Euler obstruction
critical points
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Summary:We relate the Brasselet number of a complex analytic function-germ defined on a complex analytic set to the critical points of its real part on the regular locus of the link. Similarly we give a new characterization of the Euler obstruction in terms of the critical points on the regular part of the link of the projection on a generic real line. As a corollary, we obtain a new proof of the relation between the Euler obstruction and the Gauss–Bonnet measure, conjectured by Fu.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:2522-0144
2197-9847
DOI:10.1007/s40687-024-00426-1