{"publisher":"ACM","publication_status":"published","doi":"10.1145/2582112.2582167","corr_author":"1","scopus_import":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)."}],"author":[{"full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","first_name":"Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"oa":1,"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","language":[{"iso":"eng"}],"year":"2014","publication":"Proceedings of the Annual Symposium on Computational Geometry","department":[{"_id":"HeEd"}],"month":"06","date_updated":"2024-10-09T20:55:37Z","conference":{"location":"Kyoto, Japan","end_date":"2014-06-11","name":"SoCG: Symposium on Computational Geometry","start_date":"2014-06-08"},"title":"The morse theory of Čech and Delaunay filtrations","day":"01","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","type":"conference","page":"484 - 490","date_published":"2014-06-01T00:00:00Z","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7"}],"status":"public","quality_controlled":"1","_id":"2155","publist_id":"4851","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1312.1231"}],"ec_funded":1,"citation":{"short":"U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 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.","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>","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."},"date_created":"2018-12-11T11:56:01Z","oa_version":"Submitted Version"}