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Complements of subspace arrangements. (English) Zbl 0795.52003
Summary: Let $$V$$ be a finite-dimensional vector space over the real or complex numbers. A subspace arrangement $${\mathcal A}$$ is a finite set of affine subspaces in $$V$$. There is no assumption on the dimension of the elements of $${\mathcal A}$$. Let $$M({\mathcal A})=V\backslash\bigcup_{x\in{\mathcal A}}X$$ be the complement. In this note we use the face poset of a real hyperplane arrangement to construct for all subspace arrangements $${\mathcal A}$$ a finite simplicial complex $${\mathbf M}({\mathcal A})$$ of the homotopy type of $$M({\mathcal A})$$. It is determined by combinatorial data.

##### MSC:
 52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry) 57R05 Triangulating