---
_id: '1072'
abstract:
- lang: eng
  text: Given a finite set of points in Rn and a radius parameter, we study the Čech,
    Delaunay–Čech, Delaunay (or alpha), and Wrap complexes in the light of generalized
    discrete Morse theory. Establishing the Čech 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.
acknowledgement: 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”.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Ulrich
  full_name: Bauer, Ulrich
  id: 2ADD483A-F248-11E8-B48F-1D18A9856A87
  last_name: Bauer
  orcid: 0000-0002-9683-0724
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
citation:
  ama: Bauer U, Edelsbrunner H. The Morse theory of Čech and delaunay complexes. <i>Transactions
    of the American Mathematical Society</i>. 2017;369(5):3741-3762. doi:<a href="https://doi.org/10.1090/tran/6991">10.1090/tran/6991</a>
  apa: Bauer, U., &#38; Edelsbrunner, H. (2017). The Morse theory of Čech and delaunay
    complexes. <i>Transactions of the American Mathematical Society</i>. American
    Mathematical Society. <a href="https://doi.org/10.1090/tran/6991">https://doi.org/10.1090/tran/6991</a>
  chicago: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and
    Delaunay Complexes.” <i>Transactions of the American Mathematical Society</i>.
    American Mathematical Society, 2017. <a href="https://doi.org/10.1090/tran/6991">https://doi.org/10.1090/tran/6991</a>.
  ieee: U. Bauer and H. Edelsbrunner, “The Morse theory of Čech and delaunay complexes,”
    <i>Transactions of the American Mathematical Society</i>, vol. 369, no. 5. American
    Mathematical Society, pp. 3741–3762, 2017.
  ista: Bauer U, Edelsbrunner H. 2017. The Morse theory of Čech and delaunay complexes.
    Transactions of the American Mathematical Society. 369(5), 3741–3762.
  mla: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay
    Complexes.” <i>Transactions of the American Mathematical Society</i>, vol. 369,
    no. 5, American Mathematical Society, 2017, pp. 3741–62, doi:<a href="https://doi.org/10.1090/tran/6991">10.1090/tran/6991</a>.
  short: U. Bauer, H. Edelsbrunner, Transactions of the American Mathematical Society
    369 (2017) 3741–3762.
date_created: 2018-12-11T11:49:59Z
date_published: 2017-05-01T00:00:00Z
date_updated: 2025-04-15T08:37:54Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/tran/6991
ec_funded: 1
external_id:
  arxiv:
  - '1312.1231'
  isi:
  - '000398030400024'
intvolume: '       369'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1312.1231
month: '05'
oa: 1
oa_version: Preprint
page: 3741 - 3762
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '318493'
  name: Topological Complex Systems
publication: Transactions of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '6311'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Morse theory of Čech and delaunay complexes
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 369
year: '2017'
...