Introdução à teoria de homotopia: o grupo fundamental

Abstract

The algebraic topology is a branch of mathematics which the main goal is to solve problems of geometric / topological nature with the aid of Algebra. The homotopy theory is one of the most important topics of the algebraic topology, where we highlight the notion of fundamental group of a topological space X, which consists of extract information about a topological space X through closed paths (loops) in X. Such group is a topological invariant and homotopic, that is, if two topological spaces are homeomorphic or have the same homotopy type, then their fundamental groups are isomorphic. This group is a very useful tool for deciding when two topological spaces are not homeomorphic. In this paper, we make an introduction to homotopy theory of loops, defining the fundamental group of a topological space, we study some of its properties and present examples of the fundamental group of some spaces.