Topological stability through extremely tame retractions
type: Item
instance of: scholarly article
title: Topological stability through extremely tame retractions
zbMATH Open document ID: 1245.57033
author: Aasa Feragen
published in: Topology and its Applications
publication date: 2012-03-02T00:00:00Z
review text: Smooth stability of a smooth map germ \(f:(\mathbb R^n,0) \to (\mathbb R^p,0)\) is equivalent to the following property. For every unfolding \(F:(\mathbb R^{n+d},0) \to (\mathbb R^{p+d},0)\) there is a pair of smooth retraction germs \(r:(\mathbb R^{n+d},0)\to (\mathbb R^n,0)\) and \(s:(\mathbb R^{p+d},0)\to (\mathbb R^p,0)\) such that \(f\circ r=s \circ F\). The blind translation of the above characterization does not hold for topological stability, only if one considers so-called tame retractions. The paper under review studies a special class of tame retractions, the extremely tame retractions. By proving properties (e.g. functoriality) of extremely tame retractions the author builds up a nice toolbox to study them, and shows several non-trivial examples, involving the E and Z series of singularities.
reviewed by: Richárd Rimányi
Mathematics Subject Classification ID: 57R45
Mathematics Subject Classification ID: 58K60
Mathematics Subject Classification ID: 58K25
zbMATH DE Number: 6011297
zbMATH Keywords: topological stability
zbMATH Keywords: tame retractions
zbMATH Keywords: E-series
zbMATH Keywords: Z-series
Wikidata QID: Q62012876
MaRDI profile type: Publication
full work available at URL: j.topol.2011.09.020
OpenAlex ID: W1976592173
cites work: Universal topological stratification for the Pham example
cites work: Q4308150
cites work: Q4662449
cites work: Q3654143
cites work: Q4320141
cites work: On the semi-universal deformation of a simple-elliptic hypersurface singularity. I: Unimodularity
DOI: 10.1016/J.TOPOL.2011.09.020
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description: scientific article; zbMATH DE number 6011297