Tópicos de topologia algébrica e o grupo fundamental do círculo

• Autor(a) principal: Sousa, Layana Oliveira
• Data de Publicação: 2018
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UFU
• Texto Completo: https://repositorio.ufu.br/handle/123456789/22063
• topic: Espaços topológicos; Grupo fundamental; Homotopia; Topological Spaces; Fundamental Group; Homotopy; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work, we present the introductory study to the fundamental group, which can be an important tool to answer one of the main questions of topology: if two spaces (or surfaces) are homeomorphic or not. Initially, we approach basics concepts of topological spaces necessary for the following study: homotopy between applications and, more precisely, between paths. Subsequently, we verify that the equivalence classes formed by homotopic closed paths provide a group-specific structure for each space. In a second moment, we calculate the fundamental group of the unit circle. We also present, using the mentioned tools, a demonstration for the Fundamental Theorem of Algebra.