---
OA_place: publisher
OA_type: gold
_id: '22000'
abstract:
- lang: eng
  text: '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.'
article_number: 93:1-93:22
article_processing_charge: Yes
arxiv: 1
author:
- first_name: Raphaël
  full_name: Tinarrage, Raphaël
  id: 40ebcc9d-905f-11ef-bf0a-dc475da8a04e
  last_name: Tinarrage
  orcid: 0000-0002-1404-1095
citation:
  ama: 'Tinarrage R. Simplicial approximation to CW complexes with spherical Delaunay
    triangulations. In: <i>42nd International Symposium on Computational Geometry</i>.
    Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.93">10.4230/LIPIcs.SoCG.2026.93</a>'
  apa: 'Tinarrage, R. (2026). Simplicial approximation to CW complexes with spherical
    Delaunay triangulations. In <i>42nd International Symposium on Computational Geometry</i>
    (Vol. 367). New Brunswick, NJ, United States: Schloss Dagstuhl - Leibniz-Zentrum
    für Informatik. <a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.93">https://doi.org/10.4230/LIPIcs.SoCG.2026.93</a>'
  chicago: Tinarrage, Raphaël. “Simplicial Approximation to CW Complexes with Spherical
    Delaunay Triangulations.” In <i>42nd International Symposium on Computational
    Geometry</i>, Vol. 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.
    <a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.93">https://doi.org/10.4230/LIPIcs.SoCG.2026.93</a>.
  ieee: R. Tinarrage, “Simplicial approximation to CW complexes with spherical Delaunay
    triangulations,” in <i>42nd International Symposium on Computational Geometry</i>,
    New Brunswick, NJ, United States, 2026, vol. 367.
  ista: 'Tinarrage R. 2026. Simplicial approximation to CW complexes with spherical
    Delaunay triangulations. 42nd International Symposium on Computational Geometry.
    SoCG: Symposium on Computational Geometry vol. 367, 93:1-93:22.'
  mla: Tinarrage, Raphaël. “Simplicial Approximation to CW Complexes with Spherical
    Delaunay Triangulations.” <i>42nd International Symposium on Computational Geometry</i>,
    vol. 367, 93:1-93:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026,
    doi:<a href="https://doi.org/10.4230/LIPIcs.SoCG.2026.93">10.4230/LIPIcs.SoCG.2026.93</a>.
  short: R. Tinarrage, in:, 42nd International Symposium on Computational Geometry,
    Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.
conference:
  end_date: 2026-06-05
  location: New Brunswick, NJ, United States
  name: 'SoCG: Symposium on Computational Geometry'
  start_date: 2026-06-02
corr_author: '1'
das_tickbox: '0'
date_created: 2026-06-14T22:01:43Z
date_published: 2026-05-27T00:00:00Z
date_updated: 2026-06-22T11:28:26Z
day: '27'
ddc:
- '500'
department:
- _id: UlWa
doi: 10.4230/LIPIcs.SoCG.2026.93
external_id:
  arxiv:
  - '2112.07573'
file:
- access_level: open_access
  checksum: a468edad327962309688aa78678138da
  content_type: application/pdf
  creator: dernst
  date_created: 2026-06-22T07:53:13Z
  date_updated: 2026-06-22T07:53:13Z
  file_id: '22111'
  file_name: 2026_LIPIcSSoCG_Tinarrage.pdf
  file_size: 1436035
  relation: main_file
  success: 1
file_date_updated: 2026-06-22T07:53:13Z
has_accepted_license: '1'
intvolume: '       367'
keyword:
- Triangulation of manifolds
- Simplicial approximation
- CW complexes
- Delaunay complexes
- List homomorphism problem
- Topological Data Analysis
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '05'
oa: 1
oa_version: Published Version
publication: 42nd International Symposium on Computational Geometry
publication_identifier:
  eissn:
  - 1868-8969
  isbn:
  - '9783959774185'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
  link:
  - relation: software
    url: https://doi.org/10.5281/zenodo.19251455
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: yes
title: Simplicial approximation to CW complexes with spherical Delaunay triangulations
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 367
year: '2026'
...