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Differential forms and applications

Grant number: 21/01817-7
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): April 01, 2021
Effective date (End): December 31, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Raimundo Nonato Araújo dos Santos
Grantee:Victor Zaher Cabral Cordeiro
Home 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.