Geometry & Topology

Definable triangulations with regularity conditions

Małgorzata Czapla

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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.

Article information

Source
Geom. Topol., Volume 16, Number 4 (2012), 2067-2095.

Dates
Received: 26 February 2011
Revised: 18 March 2012
Accepted: 23 April 2012
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732479

Digital Object Identifier
doi:10.2140/gt.2012.16.2067

Mathematical Reviews number (MathSciNet)
MR3033513

Zentralblatt MATH identifier
1375.14188

Subjects
Primary: 14P05: Real algebraic sets [See also 12D15, 13J30] 14P10: Semialgebraic sets and related spaces 32B20: Semi-analytic sets and subanalytic sets [See also 14P15] 32B25: Triangulation and related questions

Keywords
Weakly Lipschitz mapping definable triangulation Whitney (B) condition Verdier condition

Citation

Czapla, Małgorzata. Definable triangulations with regularity conditions. Geom. Topol. 16 (2012), no. 4, 2067--2095. doi:10.2140/gt.2012.16.2067. https://projecteuclid.org/euclid.gt/1513732479


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