The Euler obstruction and generalizations

• Grant number: 15/25191-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: September 01, 2016
• End date: September 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Nivaldo de Góes Grulha Júnior
• Grantee: Hellen Monção de Carvalho Santana
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 14/00304-2 - Singularities of differentiable mappings: theory and applications, AP.TEM
• Associated scholarship(s): 17/18543-1 - Euler obstruction and generalizations, BE.EP.DR

Abstract

The Euler obstruction, defined by MacPherson, is an invariant rised as a tool in the study of characteristic class of singular varieties. Brasselet, Massey, Parameswaran and Seade presented a generalization of this concept, associated with a function with isolated singularity, defined on a singular variety, called the Euler obstruction of f. More recently, Dutertre and Grulha gave another generalization, called the number of Brasselet. This in turn is well-defined even when f has non-isolated singularity. The aim of thhis project is study the Euler obstruction and these generalizations.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

SANTANA, HELLEN. Brasselet Number and Function-Germs with a One-Dimensional Critical Set. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 52, n. 2, JUN 2020. (15/25191-9, 17/18543-1)

GRULHA JR, NIVALDO G. JR; RUIZ, CAMILA M.; SANTANA, HELLEN. The geometrical information encoded by the Euler obstruction of a map. INTERNATIONAL JOURNAL OF MATHEMATICS, v. 33, n. 04, p. 17-pg., 2022-03-01. (19/21181-0, 15/25191-9)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SANTANA, Hellen Monção de Carvalho. Euler obstruction and generalizations. 2019. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.