Normal triangulations in o-minimal structures

2007/10/30 by Elías Baro, Elias Baro, Baro, Elias · 2 citations
Computer Science · Mathematics · #03C64 #32B25 #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Topological and Geometric Data Analysis #math.LO #msc:03C64 #msc:32B25

paper · pdf · doi:10.48550/arxiv.0710.5718

arxiv created 2007/10/30 · openalex publication_date 2007/10/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We work over an o-minimal expansion of a real closed field R. Given a closed simplicial complex K and a finite number of definable subsets of its realization |K| in R we prove that there exists a triangulation (K',f) of |K| compatible with the definable subsets such that K' is a subdivision of K and f is definably homotopic to the identity on |K|.

Cited by

• Locally definable homotopy
• On o-minimal homotopy groups

Related

• Triangulation in o-minimal fields with standard part map
• Differentiable approximation of continuous definable maps that preserves the image
• Vertex-Minimal Triangulation of Complexes with Homology
• The structure on the real field generated by the standard part map on an o-minimal expansion of a real closed field
• Definable quotients in locally o-minimal structures