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Conformal Geometry applied to the problem of global injectivity

Grant number: 19/22762-6
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): December 01, 2019
Effective date (End): November 30, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Francisco Braun
Grantee:Rodrigo Thomaz da Silva
Home 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.

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