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Topological triviality of a family of zero-sets. (English) Zbl 0658.58011
As stated in the authors’ abstract, the paper gives conditions on a mapping F: $$U\times R^ k\to K^ p$$ $$(U\subset K^ n$$ open, $$K={\mathbb{R}}$$ or $${\mathbb{C}})$$ such that the family $$F_ t^{-1}(0)$$ is a topologically trivial family. The authors consider ‘admissible’ families, which are deformations of homogeneous polynomial maps, and show that they are locally topological trivial at the origin.
Using their result they are able to simplify the proof of a counterexample to a conjecture of Thom concerning the number of topologically different realizations of a given jet, contained in a paper of S. Koike and W. Kucharz [C. R. Acad. Sci., Paris, Sér. A 288, 457-459 (1979; Zbl 0404.58002)].
Reviewer: J.Timourian

##### MSC:
 58C25 Differentiable maps on manifolds 58A20 Jets in global analysis 57R45 Singularities of differentiable mappings in differential topology
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##### References:
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