LIPSCHITZ TRIANGULATIONS

摘要

In this paper 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.