Deformation retracts of Stein spaces
type: Item
instance of: scholarly article
title: Deformation retracts of Stein spaces
zbMATH Open document ID: 0883.32008
author: Helmut A. Hamm
author: Nicolae Mihalache
published in: Mathematische Annalen
publication date: 1998-03-01T00:00:00Z
review text: Let \(X\) be an \(n\)-dimensional Stein space. It was proved by \textit{H. Hamm} [J. Reine Angew. Math. 338, 121-135 (1983; Zbl 0491.32010); J. Reine Angew. Math. 364, 1-9 (1986; Zbl 0567.32005)], \textit{M.Goresky} and \textit{R. MacPherson} [Stratified Morse Theory. (Springer, Berlin, Heidelberg) (1988; Zbl 0639.14012)] that \(X\) has the homotopy type of a CW-complex of dimension \(\leqq n;\) in the algebraic case this was proved by \textit{K. Karchyauskas} [Homotopy properties of complex algebraic sets, Studies in Topology, Steklov Institute (1979)] with the additional conclusion that the CW-complex is finite. It is therefore natural to ask if there exists a subset \(\mathcal Q\) of \(X\) with the same topological properties like \(X,\) for instance \(\mathcal Q\) is a strong definition retract of \(X,\) and \(\mathcal Q\) is a CW-complex of dimension \(\leqq n.\) The main result of the paper is: There exists a closed subanalytic subset \(\mathcal Q\) of \(X,\) dim\(\mathcal Q\leqq n,\) such that \(\mathcal Q\) is a strong deformation retract of \(X.\) If \(X\) is affine algebraic then \(\mathcal Q\) can be chosen to be compact.
Mathematics Subject Classification ID: 32C18
Mathematics Subject Classification ID: 32E10
zbMATH DE Number: 1057242
zbMATH Keywords: topology of analytic spaces
zbMATH Keywords: Stein spaces
MaRDI profile type: Publication
full work available at URL: s002080050078
OpenAlex ID: W2048148882
DOI: 10.1007/S002080050078
description: scientific article; zbMATH DE number 1057242