The Morse theory of Čech and delaunay complexes Journal Article

Author(s): Bauer, Ulrich; Edelsbrunner, Herbert
Article Title: The Morse theory of Čech and delaunay complexes
Affiliation IST Austria
Abstract: Given a finite set of points in R n and a radius parameter, we study the ˇ Cech, Delaunay– ˇ Cech, Delaunay (or alpha), and Wrap complexes in the light of generalized discrete Morse theory. Establishing the ˇ Cech and Delaunay complexes as sublevel sets of generalized discrete Morse functions, we prove that the four complexes are simple-homotopy equivalent by a sequence of simplicial collapses, which are explicitly described by a single discrete gradient field.
Journal Title: Transactions of the American Mathematical Society
Volume: 369
Issue 5
ISSN: 1088-6850
Publisher: American Mathematical Society  
Date Published: 2017-05-01
Start Page: 3741
End Page: 3762
DOI: 10.1090/tran/6991
Notes: This research has been supported by the EU project Toposys(FP7-ICT-318493-STREP), by ESF under the ACAT Research Network Programme, by the Russian Government under mega project 11.G34.31.0053, and by the DFG Collaborative Research Center SFB/TRR 109 “Discretization in Geometry and Dynamics”.
Open access: no
IST Austria Authors
  1. Ulrich Bauer
    12 Bauer
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