×

The unfolding and determinacy theorems for subgroups of \({\mathcal A}\) and \({\mathcal K}\). (English) Zbl 0545.58010

Mem. Am. Math. Soc. 306, 88 p. (1984).
The versality theorem and the finite determinacy theorem are shown to be valid for a large class of equivalence relations on map germs. These equivalence relations are induced by geometrically defined subgroups of \({\mathcal A}\) (left-right equivalence group) or \({\mathcal K}\) (contact equivalence group). The methods are mostly algebraic, consisting of an extension of the preparation theorems to systems of rings. Some examples are discussed, among which the model for symmetry breaking in equations proposed by M. Golubitsky and D. Schaeffer [Proc. Symp. Pure Math. 40, Part 1, 499-515 (1983; Zbl 0535.58010)]. A survey (with the same title), by the author can be found in the volume mentioned above.
Reviewer: A.Dimca

MSC:

58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
14B10 Infinitesimal methods in algebraic geometry

Citations:

Zbl 0535.58010
PDFBibTeX XMLCite
Full Text: DOI