Abstract
In this Note we give a sketch of the proof of a theorem which is a bilipschitz version of Hardt's theorem. Given a family definable in an o-minimal structure Hardt's theorem states the existence (for generic parameters) of a trivialization which is definable in the o-minimal structure. We show that, for a polynomially bounded o-minimal structure, there exists such an isotopy which is bilipschitz. The proof is inspired by Bochnak et al. [Géométrie Algébrique Réelle, Springer-Verlag, 1987]. and involves the construction of ‘Lipschitz triangulations’ which are defined in this Note. The complete proof of existence will appear later. To cite this article: G. Valette, C. R. Acad. Sci. Paris, Ser. I 340 (2005).
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