Damon, James 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 Cited in 5 ReviewsCited in 44 Documents MSC: 58C25 Differentiable maps on manifolds 58K99 Theory of singularities and catastrophe theory 14B10 Infinitesimal methods in algebraic geometry Keywords:unfolding; versality theorem; finite determinacy theorem; preparation theorems Citations:Zbl 0535.58010 PDFBibTeX XMLCite \textit{J. Damon}, The unfolding and determinacy theorems for subgroups of \({\mathcal A}\) and \({\mathcal K}\). Providence, RI: American Mathematical Society (AMS) (1984; Zbl 0545.58010) Full Text: DOI