Every finitely presented group is the \(\pi_ 1\) of some two dimensional Stein space
type: Item
instance of: scholarly article
title: Every finitely presented group is the \(\pi_ 1\) of some two dimensional Stein space
zbMATH Open document ID: 0832.32006
DOI: 10.1007/BF01459749
published in: Mathematische Annalen
publication date: 1994-06-14T00:00:00Z
full work available at URL: https://eudml.org/doc/165184
review text: The author proves the following main result: ``Let \(G\) be any finitely presented group. Then there exists a two-dimensional Stein space \(X\) with \(\pi_1 (X) = G\).'' The proof has two steps. In the first step one constructs a two-dimensional real algebraic set in some \(\mathbb{R}^N\) with \(\pi_1 (A) = G\). In the second step one constructs special neighbourhoods for real analytic spaces. Then \(X\) is taken to be an open Stein neighbourhood of \(A\) in a complexification of \(A\) such that \(A\) is a deformation retract of \(X\).
reviewed by: Vasile Brînzănescu
Mathematics Subject Classification ID: 32C05
Mathematics Subject Classification ID: 32C18
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 14P15
zbMATH DE Number: 562494
zbMATH Keywords: special neighbourhoods for real analytic spaces
zbMATH Keywords: fundamental group
zbMATH Keywords: Stein space
author: Nicolae Mihalache
MaRDI profile type: Publication
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OpenAlex ID: W2050595315
description: scientific article; zbMATH DE number 562494