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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.

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