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Simplicial Approximation to CW Complexes with Spherical Delaunay Triangulations

Author Raphaël Tinarrage

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LIPIcs.SoCG.2026.93.pdf
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ACM Subject Classification
  • Mathematics of computing → Mesh generation
  • Mathematics of computing → Combinatoric problems
  • Mathematics of computing → Algebraic topology
  • Mathematics of computing → Mathematical software performance
Keywords
  • Triangulation of manifolds
  • Simplicial approximation
  • CW complexes
  • Delaunay complexes
  • List homomorphism problem
  • Topological Data Analysis

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Abstract

Simplicial approximation provides a framework for constructing simplicial complexes that are homotopy equivalent to a given manifold, provided a CW structure is explicitly known. However, its conventional implementation quickly becomes intractable on a computer: barycentric subdivision produces poorly shaped simplices, and the star condition introduces many vertices. To address these limitations, this article develops a subdivision scheme based on spherical Delaunay triangulations, which attains better refinement properties than barycentric subdivisions. Moreover, the star condition is reframed as two independent problems, one geometric and the other combinatorial, respectively tackled in the language of locally equiconnected spaces and the list homomorphism problem, allowing an exponential reduction in the number of vertices. Via a prototype implementation, we obtain simplicial complexes homotopy equivalent to Grassmannians and Stiefel manifolds up to dimension 5.

Cite As Get BibTex

Raphaël Tinarrage. Simplicial Approximation to CW Complexes with Spherical Delaunay Triangulations. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 93:1-93:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.93

Author Details

Raphaël Tinarrage
  • Institute of Science and Technology Austria, Klosterneuburg, Austria

Supplementary Materials

References

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