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Characterizations of finitely determined equivariant map germs. (English) Zbl 0582.58003
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.

58A20 Jets in global analysis
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