conference paper published yes Ulrich Bauer author 2ADD483A-F248-11E8-B48F-1D18A9856A870000-0002-9683-0724 Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 HeEd department SoCG: Symposium on Computational Geometry Topological Complex Systems project 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). ACM2014Kyoto, Japan eng 1312.123110.1145/2582112.2582167 484 - 490 U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 484–490. 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> 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. 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. 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>. 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>. 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> 21552018-12-11T11:56:01Z2025-06-11T07:58:27Z