The morse theory of Čech and Delaunay filtrations - Bauer, Ulrich; Edelsbrunner, Herbert; SoCG: Symposium on Computational Geometry; Topological Complex Systems (Proceedings of the Annual Symposium on Computational Geometry, 2014)
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).
published
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Keywords: conference paper