The Poincaré-Hopf Theorem

• Grant number: 17/08540-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2017
• End date: May 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Maria Aparecida Soares Ruas
• Grantee: Edmundo Bernardo de Castro Martins
• 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): 18/13682-6 - Poincaré-Hopf type theorems for vector fields and 1-forms on singular varieties, BE.EP.IC

Abstract

We will introduce the central ideas of analysis and topology to prepare the student to develop a solid background on vector fields, to prove the Poincaré-Hopf Theorem. (AU)