Infinite determinacy of equivariant map-germs
type: Item
instance of: scholarly article
title: Infinite determinacy of equivariant map-germs
zbMATH Open document ID: 0546.58013
DOI: 10.1007/BF01455928
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163997
review text: In an important recent paper of Wilson, the equivalence of the following conditions on a map-germ f is proved (under the assumptions that f is analytic and of finite singularity type): that f is determined up to equivalence by its Taylor series; that the tangent space to the orbit of f contains all flat functions; and that f is stable in a punctured neighbourhood of the origin. The object of this paper is to extend these arguments to cover the equivariant case. The proofs follow the earlier ones fairly closely once the appropriate machinery is set up. This is mostly contained in the preceding paper [Equivariant jets] though we also need a section on equivariant construction lemmas. A final paragraph contains a brief discussion of finite \(C^ k\) determinacy in the easier cases.
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
Mathematics Subject Classification ID: 57R45
zbMATH DE Number: 3870257
zbMATH Keywords: map-germ
zbMATH Keywords: flat functions
zbMATH Keywords: Equivariant jets
zbMATH Keywords: \(C^ k\) determinacy
author: C. T. C. Wall
MaRDI profile type: Publication
cites work: Determinacy of C μ Map-Germs with Respect to a C q -Contact Equivalence
cites work: Stability of \(C^ \infty\) mappings. III: Finitely determined map germs
cites work: Faisceaux analytiques semi-cohérents
cites work: Applications des faisceaux analytiques sémi-cohérents aux fonctions différentiables
cites work: Q3744922
cites work: Infinitely Determined Mapgerms
cites work: Mapgerms infinitely determined with respect to right-left equivalence
OpenAlex ID: W1994685906
Recommended article: Q3744922
Recommended article: Infinite relative determinacy of smooth map-germs
Recommended article: Characterizations of finitely determined equivariant map germs
Recommended article: Relative infinite determinacy for map-germs
Recommended article: \({\mathcal G}_{q,k}\)-determinacy of \(C^{\infty}\) map-germs
Recommended article: Germs of infinite determinacy in smooth classes
Recommended article: A Criterion for Finite Topological Determinacy of Map-Germs
Recommended article: Q4030632
description: scientific article; zbMATH DE number 3870257