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A comparison of Vassiliev and Ziegler-Zivaljevic models for homotopy types of subspace arrangements

Dmitry N. Kozlov
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Abstract

In 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.

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Dmitry N. Kozlov. 2001-10-25. A comparison of Vassiliev and Ziegler-Zivaljevic models for homotopy types of subspace arrangements. https://arxiv.org/abs/math/0110279

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