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Global Euler obstruction, global Brasselet numbers and critical points

Part of: Theory of singularities and catastrophe theory Analytic spaces Local theory

Published online by Cambridge University Press:  14 May 2019

Nicolas Dutertre  and
Nivaldo G. Grulha Jr.
Nicolas Dutertre
Affiliation:
Laboratoire angevin de recherche en mathématiques, LAREMA, UMR6093, CNRS, UNIV. Angers, SFR MathStic, 2 Bd Lavoisier 49045 Angers Cedex 01, France (nicolas.dutertre@univ-angers.fr)
Nivaldo G. Grulha Jr.
Affiliation:
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 (njunior@icmc.usp.br)
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Abstract

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.

Keywords

Euler obstructionglobal Euler obstructionconstructible functionsMorsefications

MSC classification

Primary: 14B05: Singularities
Secondary: 32C18: Topology of analytic spaces 58K45: Singularities of vector fields, topological aspects
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 5 , October 2020 , pp. 2503 - 2534
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Copyright
Copyright © Royal Society of Edinburgh 2019

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