2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110271For a smooth manifold M obtained as an embedding torus, A U Cx[-1,1], we consider the ordered configuration space F_k(M) of k distinct points in M. We show that there is a homotopical cubical resolution of F_k(M) defined from the configuration spaces of A and C. From it, we deduce a universal method for the computation of the pure braid groups of a manifold. We illustrate the method in the case of the Mobius band.25 pagesAlgebraic TopologyGeometric Topology55R80; 20F36; 18A30text