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