On the fundamental group of the complement of arrangements
type: Item
instance of: scholarly article
title: On the fundamental group of the complement of arrangements
zbMATH Open document ID: 0863.57002
author: Nguyen Viet Dung
published in: Kodai Mathematical Journal
publication date: 1997-06-10T00:00:00Z
review text: The author describes a method to compute a presentation of the fundamental group of the complement of the union of a finite arrangement of hyperplanes in \(\mathbb{C}^n\) having real defining equations. The method involves the notion of ``1-codimensionally regular CW-semicomplex'', introduced in previous work of author. This decomposition of the hyperplane complement bears some similarity to known regular CW-complexes associated with arrangements, but is smaller, retaining just enough structure for the fundamental group calculation. The author's approach does not require the choice of a generic 3-dimensional section, as in the Randell-Arvola presentation. The resulting presentation does not appear to differ substantially from the presentation obtained by \textit{M. Salvetti} [Invent. Math. 88, 603-618 (1987; Zbl 0594.57009)].
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 52C35
zbMATH DE Number: 729234
zbMATH Keywords: arrangement
zbMATH Keywords: hyperplanes
zbMATH Keywords: complexification
zbMATH Keywords: fundamental group
reviewed by: Michael Falk
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138040035
OpenAlex ID: W2157439558
cites work: The fundamental group of the complement of an arrangement of complex hyperplanes
cites work: The fundamental groups of the spaces of regular orbits of the affine Weyl groups
cites work: Topology of the complement of real hyperplanes in \({\mathbb C}^ N\)
DOI: 10.2996/KMJ/1138040035
description: scientific article; zbMATH DE number 729234