Topology and geometry of real and complex singularities

• Grant number: 18/09297-0
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: August 01, 2018
• End date: August 21, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Nivaldo de Góes Grulha Júnior
• Grantee: Nivaldo de Góes Grulha Júnior
• Visiting researcher: Nicolas Dutertre
• Visiting researcher institution: Université d'Angers, France
• 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

Abstract

This project has two strands. In the first one, we propose to investigate the calculation of invariants related to the study of characteristic classes such as the Euler obstruction and Brasselet number (in global and local configurations).In addition to this, the second one proposes to investigate the topology of a differentiable variety through the critical set of applications defined on such variety. In this theme, the main objective is to study the singularities of vector n-frame, searching for a local characterization, besides investigating its relations with the topology of varieties on which these n-frames are defined. (AU)