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Definable triangulations with regularity conditions

Małgorzata Czapla
Geometry & Topology 16 (2012) 2067–2095
DOI: 10.2140/gt.2012.16.2067
Abstract

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 T of regularity conditions and give a universal construction of a definable triangulation with a T condition of a definable set. This class includes the Whitney (B) and the Verdier conditions.

Keywords
Weakly Lipschitz mapping, definable triangulation, Whitney (B) condition, Verdier condition
Mathematical Subject Classification 2010
Primary: 14P05, 14P10, 32B20, 32B25
References
Publication
Received: 26 February 2011
Revised: 18 March 2012
Accepted: 23 April 2012
Published: 27 October 2012
Proposed: Walter Neumann
Seconded: Martin R Bridson, Tobias H Colding
Authors
Małgorzata Czapla
Uniwersytet Jagielloński
Instytut Matematyki
ul. Łojasiewicza 6
30-348 Kraków
Poland