Differentiable manifolds and Morse Theory

• Grant number: 25/07026-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2025
• Status: Discontinued
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Renato Ferreira de Velloso Vianna
• Grantee: Pedro Luiz Pimenta Barbosa
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 24/01351-6 - Lagrangian submanifolds - Open Gromov-Witten theory and Mirror Symmetry, AP.JP

Abstract

We will study the basic concepts of differentiable manifolds: definitions of manifolds and submanifolds, vector fields, metric, gradient vector field and examples to internilize the concepts. Then we study Morse theory, proving Morse lema and the description of a manifold as a CW complex in terms of handle attachments associated to critical points of a Morse function. In the end, we will provide a short discussion about Morse homology.