Conformal Geometry applied to the problem of global injectivity

• Grant number: 19/22762-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2019
• End date: November 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Francisco Braun
• Grantee: Rodrigo Thomaz da Silva
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

With our aim in the work of the Frederico Xavier (a preprint), named “Conformal geometry, Euler numbers, and global invertibility in higher dimensions”, we plan to study topics of differential geometry, geometry of manifolds and topology during about eight to ten months. Throughout the development of the study we will make several connections between these areas, seeking to understand all the ways of attacking problems of global infectivity with the tools gathered from these fields. Armed with all these contents, in the last months of the project we will study the already cited Xavier's article, which shows a series of results, involving several areas of Mathematics, related to the global infectivity problem.