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

2001/10/25 by Dmitry N. Kozlov
Mathematics · #math.CO #math.AT #msc:52C35 #msc:06A11 #msc:52B30

paper · pdf

published as Topology Appl. 126 (2002), no. 1-2, 119--129.

arxiv created 2001/10/25 · arxiv updated 2009/11/30

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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