Complexified real arrangements of hyperplanes
type: Item
instance of: scholarly article
title: Complexified real arrangements of hyperplanes
zbMATH Open document ID: 0731.57011
DOI: 10.1007/BF02568407
author: William A. Arvola
published in: Manuscripta Mathematica
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155617
review text: 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.
reviewed by: Selman Akbulut
Mathematics Subject Classification ID: 57Q99
zbMATH DE Number: 4209103
zbMATH Keywords: arrangement
zbMATH Keywords: simplicial complexes
zbMATH Keywords: homotopy type
MaRDI profile type: Publication
cites work: Oriented Matroids
cites work: Simplicial structures and transverse cellularity
cites work: Q5287192
cites work: Topology of the complement of real hyperplanes in \({\mathbb C}^ N\)
OpenAlex ID: W1973698788
description: scientific article; zbMATH DE number 4209103