{"title":"The morse theory of Čech and Delaunay filtrations","quality_controlled":"1","publist_id":"4851","publication":"Proceedings of the Annual Symposium on Computational Geometry","corr_author":"1","abstract":[{"lang":"eng","text":"Given a finite set of points in Rn and a positive radius, we study the Čech, Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete Morse theory. We prove that the latter three complexes are simple-homotopy equivalent. Our results have applications in topological data analysis and in the reconstruction of shapes from sampled data. Copyright is held by the owner/author(s)."}],"citation":{"mla":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Filtrations.” <i>Proceedings of the Annual Symposium on Computational Geometry</i>, ACM, 2014, pp. 484–90, doi:<a href=\"https://doi.org/10.1145/2582112.2582167\">10.1145/2582112.2582167</a>.","chicago":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Filtrations.” In <i>Proceedings of the Annual Symposium on Computational Geometry</i>, 484–90. ACM, 2014. <a href=\"https://doi.org/10.1145/2582112.2582167\">https://doi.org/10.1145/2582112.2582167</a>.","ieee":"U. Bauer and H. Edelsbrunner, “The morse theory of Čech and Delaunay filtrations,” in <i>Proceedings of the Annual Symposium on Computational Geometry</i>, Kyoto, Japan, 2014, pp. 484–490.","apa":"Bauer, U., &#38; Edelsbrunner, H. (2014). The morse theory of Čech and Delaunay filtrations. In <i>Proceedings of the Annual Symposium on Computational Geometry</i> (pp. 484–490). Kyoto, Japan: ACM. <a href=\"https://doi.org/10.1145/2582112.2582167\">https://doi.org/10.1145/2582112.2582167</a>","ista":"Bauer U, Edelsbrunner H. 2014. The morse theory of Čech and Delaunay filtrations. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 484–490.","short":"U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 484–490.","ama":"Bauer U, Edelsbrunner H. The morse theory of Čech and Delaunay filtrations. In: <i>Proceedings of the Annual Symposium on Computational Geometry</i>. ACM; 2014:484-490. doi:<a href=\"https://doi.org/10.1145/2582112.2582167\">10.1145/2582112.2582167</a>"},"publication_status":"published","date_created":"2018-12-11T11:56:01Z","main_file_link":[{"url":"http://arxiv.org/abs/1312.1231","open_access":"1"}],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","author":[{"orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","full_name":"Bauer, Ulrich","first_name":"Ulrich"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert"}],"doi":"10.1145/2582112.2582167","publisher":"ACM","month":"06","year":"2014","page":"484 - 490","conference":{"end_date":"2014-06-11","name":"SoCG: Symposium on Computational Geometry","start_date":"2014-06-08","location":"Kyoto, Japan"},"date_published":"2014-06-01T00:00:00Z","day":"01","department":[{"_id":"HeEd"}],"ec_funded":1,"external_id":{"arxiv":["1312.1231"]},"project":[{"call_identifier":"FP7","grant_number":"318493","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"type":"conference","oa_version":"Submitted Version","acknowledgement":"This research is partially supported by ESF under the ACAT Research Network Programme, and by the Russian Government under mega project 11.G34.31.0053","status":"public","language":[{"iso":"eng"}],"_id":"2155","date_updated":"2025-06-11T07:58:27Z","oa":1,"arxiv":1}