Complexidade topológica em espaços de configurações de grafos

Abstract

Since the end of the last century, the motion planning problem has acquired a mathematical framework with the concept of Farber’s topological complexity. Furthermore, with the concept of configuration spaces, we have managed to address the case of the motion of multiple bodies without collisions. In this dissertation, we will see how to calculate this numerical invariant for configuration spaces over topological graphs. To achieve this, we will make use of general techniques from General and Algebraic Topology.