Introduction to Morse Theory

• Grant number: 24/14023-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2024
• End date: February 28, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Luiz Roberto Hartmann Junior
• Grantee: Matheus Henrique Ferreira de Melo dos Santos
• 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

We propose an in-depth study of Morse Theory, focusing on the Fundamental Theorem of this theory. To this end, we will explore essential tools from Riemannian Geometry and Algebraic Topology, which are fundamental for understanding the Fundamental Theorem of Morse Theory.