  For 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.
