Work

The distance function to a finite set is a topological Morse function

Year: 2024

Type: preprint

Abstract: In this short note, we show that the distance function to any finite set $X\subset \mathbb{R}^n$ is a topological Morse function, regardless of whether $X$ is in general position. We also precisely characterize its topological critical points and their indices, and relate them to the differential critical points of the function.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2407.15578

Author: Arnal, Charles

Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay, DATASHAPE: Comprendre la forme des données

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4400870671

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