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Lipschitz triangulations. (English) Zbl 1154.14323
Summary: We introduce a new tool called “Lipschitz triangulations”, which gives combinatorially all information about the metric type. We show the existence of such triangulations for semi-algebraic sets. As a consequence we obtain a bi-Lipschitz version of Hardt’s theorem. Hardt’s theorem states that, given a family definable in an \(o\)-minimal structure, there exists (generically) a trivialization which is definable in this \(o\)-minimal structure. We show that, for a polynomially bounded \(o\)-minimal structure, there exists such an isotopy which is bi-Lipschitz as well.
Reviewer: Reviewer (Berlin)

MSC:
14P05 Real algebraic sets
14P15 Real-analytic and semi-analytic sets
32B25 Triangulation and topological properties of semi-analytic andsubanalytic sets, and related questions
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