Euler obstruction, Brasselet number and critical points

• Published in: Research in the mathematical sciences Vol. 11; no. 2
• Main Author: Dutertre, Nicolas
• Format: Journal Article
• Language: English
• 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
• ISSN: 2522-0144; 2197-9847
• DOI: 10.1007/s40687-024-00426-1

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...