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

Grant number: 18/13682-6
Support type:Scholarships abroad - Research Internship - Scientific Initiation
Effective date (Start): September 01, 2018
Effective date (End): December 31, 2018
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Maria Aparecida Soares Ruas
Grantee:Edmundo Bernardo de Castro Martins
Supervisor abroad: Nicolas Dutertre
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Research place: 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)

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