Definable triangulations with regularity conditions

Czapla, Małgorzata¹

¹ Uniwersytet Jagielloński, Instytut Matematyki, ul. Łojasiewicza 6, 30-348 Kraków, Poland

Geometry & topology, Tome 16 (2012) no. 4, pp. 2067-2095.

Résumé

We prove that every definable in an o-minimal structure set has a definable triangulation which is locally Lipschitz and weakly bi-Lipschitz on the natural simplicial stratification of a simplicial complex. We also distinguish a class $\mathcal{T}$ of regularity conditions and give a universal construction of a definable triangulation with a $\mathcal{T}$ condition of a definable set. This class includes the Whitney (B) and the Verdier conditions.

Détail

DOI : 10.2140/gt.2012.16.2067

Classification : 14P05, 14P10, 32B20, 32B25
Keywords: Weakly Lipschitz mapping, definable triangulation, Whitney (B) condition, Verdier condition

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