Fundamental group

• Grant number: 17/07047-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2017
• End date: July 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: João Peres Vieira
• Grantee: Matheus Eduardo Dametto Silva
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

The method of Algebraic Topology consists of describing the geometric structure of a topological space, associating to it an algebraic system, usually a group or a sequence of groups. To the continuous functions between spaces correspond homomorphisms between the groups associated to them. In this project we will develop the fundamental group. We will see, for example, that the fundamental group is a topological invariant, that is, homeomorphic spaces have fundamental isomorphic groups. We will also study important applications, such as Brouwer Fixed-Point Theorem and Borsuk-Ulam Theorem. (AU)