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Topological triviality and versality for subgroups of \(\mathcal A\) and \(\mathcal K\). II: Sufficient conditions and applications. (English) Zbl 0747.58014
In part I of this paper [Mem. Am. Math. Soc. 389, 106 p. (1988; Zbl 0665.58005)] the author obtains theorems ensuring topological triviality and versality of unfoldings.
In this paper the author applies the results obtained in part I to give answers to the topological equivalence, determinacy and versality problems. The obtained results are given by infinitesimal conditions but relative to algebraic filtration conditions on the tangent spaces of the group of diffeomorphisms and to the spaces of germs. The results are also applied to a number of problems involving the classification of finite map germs, equivariant bifurcation problems, and the equivalence of germs preserving varieties.

MSC:
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
14B07 Deformations of singularities
37G99 Local and nonlocal bifurcation theory for dynamical systems
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