Poincaré-Hopf type theorems for vector fields and 1-forms on singular varieties

• Grant number: 18/13682-6
• Support Opportunities: Scholarships abroad - Research Internship - Scientific Initiation
• Start date: September 01, 2018
• End date: December 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Maria Aparecida Soares Ruas
• Grantee: Edmundo Bernardo de Castro Martins
• Supervisor: Nicolas Dutertre
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Université d'Angers, France
• Associated to the scholarship: 17/08540-5 - The Poincaré-Hopf Theorem, BP.IC

Abstract

The idea of the project is to acquaint the student with the concept of index of vector fields and 1-forms defined on singular varieties, seeking to understand the different generalizations of the concept for such objects, based on the of the Poincaré-Hopf Index for vector fields on smooth manifolds. The main goal of the project is the investigation of different versions of the Poincaré-Hopf Theorem for vector fields and 1-forms on singular varieties, allowing a comparison between the generalizations of the concept of index and the classical Poincaré-Hopf Index. (AU)