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Global Euler obstruction, global Brasselet numbers and critical points

Published online by Cambridge University Press:  14 May 2019

Nicolas Dutertre
Laboratoire angevin de recherche en mathématiques, LAREMA, UMR6093, CNRS, UNIV. Angers, SFR MathStic, 2 Bd Lavoisier 49045 Angers Cedex 01, France (
Nivaldo G. Grulha Jr.
Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação - USP Av. Trabalhador São-carlense, 400 - Centro, Caixa Postal: 668 - CEP: 13560-970 - São Carlos - SP - Brazil (


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.

Research Article
Copyright © Royal Society of Edinburgh 2019

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