The topological degree and applications

• Grant number: 21/07192-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2021
• End date: March 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marcelo José Saia
• Grantee: Leandro de Jesus Nascimento Bacelar
• 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 an important tool of differential topology, which has been deeply used in several areas of mathematics: the topological degree theory. First, we will study some analytical results on $\mathbb{R}^n$, and then we will study the theory of manifolds. Next, we will study the concept of degree, its properties and some of its applications, such as the Brouwer fixed point Theorem and the notion of index of vector fields in manifolds.