Every finitely presented group is the \(\pi_ 1\) of some two dimensional Stein space
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 \(X\).
special neighbourhoods for real analytic spaces
scientific article; zbMATH DE number 562494
scientific article