Topics in Algebraic Topology: Homological Algebra, Singular Homology, and Applications

• Grant number: 25/20248-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2025
• End date: September 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Edivaldo Lopes dos Santos
• Grantee: Matthews Silva Vicentine
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 22/16455-6 - Algebraic, geometric, and differential topology, AP.TEM

Abstract

The aim of this research project is to address certain concepts, techniques, and applications of Algebraic Topology. Initially, the focus will be on the study of Homological Algebra, which provides the necessary prerequisites for the subsequent development of Singular Homology Theory and its applications, such as the Jordan-Brouwer Separation Theorem.