2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62492In this paper we represent the Vassiliev model for the homotopy type of the one-point compactification of subspace arrangements as a homotopy colimit of an appropriate diagram over the nerve complex of the intersection semilattice of the arrangement. Furthermore, using a generalization of simplicial collapses to diagrams of topological spaces over simplicial complexes, we construct an explicit deformation retraction from the Vassiliev model to the Ziegler-Zivaljevic model.CombinatoricsAlgebraic Topology52C35 (primary); 06A11, 52B30 (secondary)text