A comparison of Vassiliev and Ziegler-Živaljević models for homotopy types of subspace arrangements (Q1867175)

In the paper two models for the homotopy type of the one-point compactification of subspace arrangements are compared. The first model was constructed by \textit{V. A. Vassiliev} [Complements of Discriminants of Smooth Maps: Topology and Applications (1992)]. The second one by \textit{G. M. Ziegler} and \textit{R. T. Živaljević} [Math. Ann. 295, 527-548 (1993; Zbl 0792.55002)]. The author gives a presentation for the Vassiliev model as a certain homotopy colimit and then, by using a diagram-theoretic generalization of simplicial collapses, he describes a sequence of generalized collapses leading from the Vassilev model to the Ziegler-Živaljević model.