On the homotopy type of the Salvetti complexes determined by simplicial arrangements (Q1329069)

For an arrangement of hyperplanes \(H_ 1, \dots, H_ n\) through the origin in \(\mathbb{R}^ d\), let \(M\) denote \(\mathbb{C}^ d\) minus the union of the complexified hyperplanes \(\mathbb{C} \otimes H_ i\). For a simplicial arrangement, \(M\) is a \(K (\pi, 1)\)-space by a theorem of \textit{P. Deligne} [Invent. Math. 17, 273-302 (1972; Zbl 0238.20034)]. The author gives an ``oriented matroid version'' of this theorem including a discussion of the universal covering of \(M\). Another proof for oriented matroids was obtained by \textit{M. Salvetti} in Discrete Math. 113, No. 1-3, 155-177 (1993; Zbl 0774.52007).