Infinite determinacy of equivariant map-germs. (English) Zbl 0546.58013

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.


58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
57R45 Singularities of differentiable mappings in differential topology
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