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Brasselet, Jean-Paul
2022.
Handbook of Geometry and Topology of Singularities III.
p.
303.
Published online by Cambridge University Press: 14 May 2019
Let X ⊂ ℂn be an equidimensional complex algebraic set and let f: X → ℂ be a polynomial function. For each c ∈ 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.