The distance function to a finite set is a topological Morse function
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913440170246144 |
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| author | Arnal, Charles |
| author_facet | Arnal, Charles |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15578 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The distance function to a finite set is a topological Morse function Arnal, Charles Differential Geometry Computational Geometry 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. |
| title | The distance function to a finite set is a topological Morse function |
| topic | Differential Geometry Computational Geometry |
| url | https://arxiv.org/abs/2407.15578 |