2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163601The topological complexity TC(X) is a homotopy invariant which reflects the complexity of the problem of constructing a motion planning algorithm in the space X, viewed as configuration space of a mechanical system. In this paper we complete the computation of the topological complexity of the configuration space of n distinct points in Euclidean m-space for all m>1$ and n>1; the answer was previously known in the cases m=2 and m odd. We also give several useful general results concerning sharpness of upper bounds for the topological complexity.Algebraic Topology55M99, 55R80, 68T40.text