Topics on algebraic topology II

• Grant number: 20/01077-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2020
• End date: December 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alice Kimie Miwa Libardi
• Grantee: Pedro Henrique Muller Bortolucci
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
• Associated research grant: 16/24707-4 - Algebraic, geometric and differential topology, AP.TEM

Abstract

This main goal of this project is to study concepts and techniques of Algebraic Topology which will give a solid background to a student who intend to do a graduate school in this area. The student already developed, under my supervision, the following topics: fundamental group, singular homology and make calculations, by using Mayer-Vietoris sequence. This project will focus on more advanced topics: Orientation of manifolds, Singular Cohomology theory, Products, Universal coefficients theorems and the Poincaré Duality. The student was accepted to an internship at the Fourier Institute, Grenoble, France under supervision of Louis Funar.