23.01.2019 um 17:15 Uhr in 69/125:
Prof. Dr. Ulrich Bauer (Technische Universität München)
The Morse Theory of Čech and Delaunay Complexes
Given a finite set of points in ℝⁿ and a radius parameter, we consider the Čech, Delaunay–Čech, Delaunay
(alpha shape), and wrap complexes in the light of generalized discrete Morse theory. We prove that the four
complexes are simple-homotopy equivalent by a sequence of simplicial collapses, and the same is true
for their weighted versions. Our results have applications in topological data analysis and in the reconstruction
of shapes from sampled data.