Differential forms and applications

• Grant number: 21/01817-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2021
• End date: December 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Raimundo Nonato Araújo dos Santos
• Grantee: Victor Zaher Cabral Cordeiro
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 19/21181-0 - New frontiers in Singularity Theory, AP.TEM

Abstract

In this project we will develop a study of differential forms and its main applications in the geometric/topological studies of differentiable manifolds based on the references "From Calculus to Cohomology" by Madsen and Tornehave, and "Differential Forms and Applications "by Manfredo P. do Carmo. In these references the authors have introduced the main techniques and theorems in aelementary and consistent way for a first approach of the theory and for an introductory view to De Rham Cohomology and its main applications.