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math.DG2024
The distance function to a finite set is a topological Morse function
Charles Arnal
In this short note, we show that the distance function to any finite set is a topological Morse function, regardless of whether is in general position.…
cs.CG2024
Wasserstein convergence of Čech persistence diagrams for samplings of submanifolds
Charles Arnal, David Cohen-Steiner, Vincent Divol
Čech Persistence diagrams (PDs) are topological descriptors routinely used to capture the geometry of complex datasets. They are commonly compared using the Wasserstein distances $…