{"year":"2023","ddc":["510"],"abstract":[{"lang":"eng","text":"We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use."}],"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"publisher":"Springer Nature","ec_funded":1,"article_type":"original","status":"public","oa_version":"Published Version","department":[{"_id":"HeEd"}],"citation":{"ista":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. 2023. Local criteria for triangulating general manifolds. Discrete &#38; Computational Geometry. 69, 156–191.","short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, M. Wintraecken, Discrete &#38; Computational Geometry 69 (2023) 156–191.","ieee":"J.-D. Boissonnat, R. Dyer, A. Ghosh, and M. Wintraecken, “Local criteria for triangulating general manifolds,” <i>Discrete &#38; Computational Geometry</i>, vol. 69. Springer Nature, pp. 156–191, 2023.","ama":"Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. Local criteria for triangulating general manifolds. <i>Discrete &#38; Computational Geometry</i>. 2023;69:156-191. doi:<a href=\"https://doi.org/10.1007/s00454-022-00431-7\">10.1007/s00454-022-00431-7</a>","mla":"Boissonnat, Jean-Daniel, et al. “Local Criteria for Triangulating General Manifolds.” <i>Discrete &#38; Computational Geometry</i>, vol. 69, Springer Nature, 2023, pp. 156–91, doi:<a href=\"https://doi.org/10.1007/s00454-022-00431-7\">10.1007/s00454-022-00431-7</a>.","chicago":"Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, and Mathijs Wintraecken. “Local Criteria for Triangulating General Manifolds.” <i>Discrete &#38; Computational Geometry</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00454-022-00431-7\">https://doi.org/10.1007/s00454-022-00431-7</a>.","apa":"Boissonnat, J.-D., Dyer, R., Ghosh, A., &#38; Wintraecken, M. (2023). Local criteria for triangulating general manifolds. <i>Discrete &#38; Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-022-00431-7\">https://doi.org/10.1007/s00454-022-00431-7</a>"},"type":"journal_article","has_accepted_license":"1","date_created":"2023-01-16T10:04:06Z","isi":1,"article_processing_charge":"No","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"scopus_import":"1","title":"Local criteria for triangulating general manifolds","month":"01","date_updated":"2023-08-01T12:47:32Z","acknowledgement":"This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). Arijit Ghosh is supported by Ramanujan Fellowship (No. SB/S2/RJN-064/2015). Part of this work was done when Arijit Ghosh was a Researcher at Max-Planck-Institute for Informatics, Germany, supported by the IndoGerman Max Planck Center for Computer Science (IMPECS). Mathijs Wintraecken also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Austrian Science Fund (FWF): M-3073. A part of the results described in this paper were presented at SoCG 2018 and in [3]. \r\nOpen access funding provided by the Austrian Science Fund (FWF).","oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"intvolume":"        69","quality_controlled":"1","language":[{"iso":"eng"}],"page":"156-191","file_date_updated":"2023-02-02T11:01:10Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"file_id":"12488","checksum":"46352e0ee71e460848f88685ca852681","success":1,"date_created":"2023-02-02T11:01:10Z","file_name":"2023_DiscreteCompGeometry_Boissonnat.pdf","access_level":"open_access","relation":"main_file","file_size":582850,"date_updated":"2023-02-02T11:01:10Z","content_type":"application/pdf","creator":"dernst"}],"date_published":"2023-01-01T00:00:00Z","publication":"Discrete & Computational Geometry","publication_status":"published","day":"01","external_id":{"isi":["000862193600001"]},"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020"},{"name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","grant_number":"M03073"}],"doi":"10.1007/s00454-022-00431-7","author":[{"last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel"},{"first_name":"Ramsay","last_name":"Dyer","full_name":"Dyer, Ramsay"},{"first_name":"Arijit","last_name":"Ghosh","full_name":"Ghosh, Arijit"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs"}],"volume":69,"_id":"12287"}