A study of vector fields indexes: from topology to the geometry

• Grant number: 21/02951-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2021
• End date: May 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marcelo Jose Saia
• Grantee: Olavo Queiroga de Melo
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 19/21181-0 - New frontiers in Singularity Theory, AP.TEM

Abstract

One of the main goals of this project is to present the basic concepts of Vector Fields theory on Manifolds, studying the necessary elements to understand the definition of the index of a singularity as well as the important results related to this invariant. In particular, we intend to present the Poincaré-Hopf Theorem and approach how such a result connects topological elements to geometric objects.