On the homotopy type of the Salvetti complexes determined by simplicial arrangements
type: Item
instance of: scholarly article
title: On the homotopy type of the Salvetti complexes determined by simplicial arrangements
zbMATH Open document ID: 0809.52018
author: Raul Cordovil
published in: European Journal of Combinatorics
publication date: 1994-07-19T00:00:00Z
review text: 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).
Mathematics Subject Classification ID: 52C35
Mathematics Subject Classification ID: 55Q20
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 52B40
zbMATH DE Number: 597745
zbMATH Keywords: Salvetti complex
zbMATH Keywords: simplicial matroid
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
full work available at URL: eujc.1994.1022
OpenAlex ID: W2023397117
DOI: 10.1006/EUJC.1994.1022
description: scientific article; zbMATH DE number 597745