Grafos de grupos e grupos de Baumslag-Solitar generalizados

Abstract

This dissertation is an introduction to Bass-Serre theory. In low-dimensional topology the use of algebraic strategies is quite common and a very useful tool. In this context, the study of geometric group theory incorporates the main results. Within geometric group theory, Bass-Serre theory is one of the most successful theories developed in low-dimensional topology. In this study, we present the concept of graph of groups, which is strongly related to with the fundamental group of spaces. We study coverings trees, also known as Bass-Serre tree, which are related to coverings of topological spaces and we finish by studying the case of graph of groups where all the groups are infinite cyclic. The groups associated to these graph of groups are called generalized Baumslag-Solitar groups. We finish with a simplification theorem for group graphs in this case.