Global Euler obstruction, global Brasselet numbers and critical points

Abstract

Let $X\subset {\mathbb{C}}^n$ be an equidimensional complex algebraic set and let $f:X\to \mathbb{C}$ be a polynomial function. For each $c\in \mathbb{C}$, we define the global Brasselet number of $f$ at $c$, a global counterpart of the Brasselet number defined by the authors in a previous work, and the Brasselet number at infinity of $f$ at $c$. Then we establish several formulas relating these numbers to the topology of $X$ and the critical points of $f$.

References in corpus (4)

• Regularity at infinity of real mappings and a Morse-Sard theorem
• Asymptotic equisingularity and topology of complex hypersurfaces
• Global Euler obstruction and polar invariants
• Curvature and Gauss-Bonnet defect of global affine hypersurfaces