Morse Theory and Bott periodicity

• Grant number: 25/02838-9
• Support Opportunities: Scholarships in Brazil - Master
• Start date: May 01, 2025
• End date: April 30, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Renato Ferreira de Velloso Vianna
• Grantee: Renata Marques do Nascimento
• 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

The bulk of Renata Marques do Nascimento's masters project consists in the study of Morse Theory where she will address technical details both of the topological description of a smooth manifold, endowed with a Morse function, through handle attachments aquired when crossing critical values of the function, as well as, the construction of Morse-Smale-Witten homology and its equivalency with CW-homology and hence singular homology. After that, we intend to present a proof of Bott's periodicity theorem, in detail. Time allowing and if it is in Renata's interests, she can explore in her dissertation aspects of Floer theory, which is a theory in symplectic geometry related to Morse theory.