Introduction to algebraic topology: the fundamental group

• Grant number: 11/21268-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2012
• End date: December 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Maria Gorete Carreira Andrade
• Grantee: Jéssica Cristina Rossinati Rodrigues da Costa
• 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 present project is an introduction to algebraic topology with the study of some topics in homotopy theory, specifically the study of the fundamental group of a topological space X. Will be seen among other topics: definition, main properties and examples of the fundamental group, the fundamental group as a homotopic invariant, and some examples of calculation of the fundamental group of the union of two spaces. The topics will be developed in a formal way, always looking for a geometric approach, making the student feel the connection between large areas (Algebra and Topology) which we consider very important and beneficial to their training.(AU)