Complexified real arrangements of hyperplanes (Q808035)

Let V be a finite dimensional vector space over \({\mathbb{R}}\), or \({\mathbb{C}}\). A real (or complex) arrangement \({\mathcal A}\) is a finite collection of real (or complex) affine hyperplanes in V. Let \({\mathcal A}\) be a real arrangement in a real vector space V, and let M(\({\mathcal A})\) be the complement of the corresponding complex arrangement in the complexified vector space: \[ M({\mathcal A})=V\otimes {\mathbb{C}}-\cup_{H\in {\mathcal A}}H\otimes {\mathbb{C}} \] M. Salvetti and P. Orlik independently constructed finite simplicial complexes which carry the homotopy type of M(\({\mathcal A})\). Here, the author studies both of these simplicial complexes, and constructs explicit homotopy equivalence between them.