TY - JOUR
T1 - The Morse theory of Čech and Delaunay complexes
AU - Bauer, Ulrich
AU - Edelsbrunner, Herbert
N1 - Publisher Copyright:
© 2016 American Mathematical Society.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85012050410&partnerID=8YFLogxK
U2 - 10.1090/tran/6991
DO - 10.1090/tran/6991
M3 - Article
AN - SCOPUS:85012050410
SN - 0002-9947
VL - 369
SP - 3741
EP - 3762
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 5
ER -