Fundamental group and covering spaces

• Grant number: 06/07022-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2007
• End date: December 31, 2007
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ermínia de Lourdes Campello Fanti
• Grantee: Íris Andrade Rodrigues
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil

Abstract

The main objective of this project of Scientific Initiation proposed to the student Íris Andrade Rodrigues, is a study of the fundamental group and certain topics of the theory of covering spaces. Those two themes are of great importance in Algebraic Topology and will be fundamental to continue hers studies in postgraduate level, since she has interest in get her master degree in this area. This project can be considerate a continuation of the works that she has been developing under our orientation. Among the topics we point out the fundamental group of S1, classification of covering spaces, universal covering spaces, group of automorphisms of a covering space and an important application: the Borsuk - Ulam Theorem for the 2-sphere.