Characterizations of finitely determined equivariant map germs
type: Item
instance of: scholarly article
title: Characterizations of finitely determined equivariant map germs
zbMATH Open document ID: 0582.58003
DOI: 10.1007/BF01459139
published in: Mathematische Annalen
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164172
review text: This paper generalises results of Mather, characterising finitely determined map germs, to germs which are equivariant with respect to linear actions of a compact or reductive (in the real and complex cases, respectively) Lie group G. Finite determinacy is considered with respect to equivariant analogues of the groups of equivalences studied by Mather. The characterisations obtained are: (1) necessary and sufficient ''infinitesimal'' algebraic conditions for a germ to be finitely determined, (2) ''geometric criteria'' for the finite determinacy of a germ, in terms of the stability of nearby germs, and (3) a characterisation of finitely determined germs in terms of transversality conditions on the ''G-jet'' extension (introduced in the paper) of a representative of the germ. The final section considers some examples.
Mathematics Subject Classification ID: 58A20
zbMATH DE Number: 3932034
zbMATH Keywords: finitely determined map germs
zbMATH Keywords: equivariant linear actions of a compact or reductive Lie group G
zbMATH Keywords: transversality conditions
zbMATH Keywords: ''G-jet'' extension
author: R. M. Roberts
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3932034