The morse theory of Čech and Delaunay filtrations Conference Paper

Author(s): Bauer, Ulrich; Edelsbrunner, Herbert
Title: The morse theory of Čech and Delaunay filtrations
Affiliation IST Austria
Abstract: 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).
Conference Title: SoCG: Symposium on Computational Geometry
Conference Dates: June 8-11, 2014
Conference Location: Kyoto, Japan
ISBN: 978-1-4503-2594-3
Publisher: ACM  
Date Published: 2014-06-01
Start Page: 484
End Page: 490
Sponsor: This research is partially supported by the Toposys project FP7- ICT-318493-STREP, by ESF under the ACAT Research Network Programme, and by the Russian Government under mega project 11.G34.31.0053
DOI: 10.1145/2582112.2582167
Open access: yes (repository)