Persistent homology of function spaces
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915298829926400 |
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| author | Block, Jonathan Manin, Fedor Weinberger, Shmuel |
| author_facet | Block, Jonathan Manin, Fedor Weinberger, Shmuel |
| contents | We can view the Lipschitz constant as a height function on the space of maps between two manifolds and ask (as Gromov did nearly 30 years ago) what its ``Morse landscape'' looks like: are there high peaks, deep valleys and mountain passes? A simple and relatively well-studied version of this question: given two points in the same component (homotopic maps), does a path between them (a homotopy) have to pass through maps of much higher Lipschitz constant? Now we also consider similar questions for higher-dimensional cycles in the space. We make this precise using the language of persistent homology and give some first results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Persistent homology of function spaces Block, Jonathan Manin, Fedor Weinberger, Shmuel Algebraic Topology Differential Geometry Metric Geometry 53C23 (Primary), 55N31, 55P62, 55S37 (Secondary) We can view the Lipschitz constant as a height function on the space of maps between two manifolds and ask (as Gromov did nearly 30 years ago) what its ``Morse landscape'' looks like: are there high peaks, deep valleys and mountain passes? A simple and relatively well-studied version of this question: given two points in the same component (homotopic maps), does a path between them (a homotopy) have to pass through maps of much higher Lipschitz constant? Now we also consider similar questions for higher-dimensional cycles in the space. We make this precise using the language of persistent homology and give some first results. |
| title | Persistent homology of function spaces |
| topic | Algebraic Topology Differential Geometry Metric Geometry 53C23 (Primary), 55N31, 55P62, 55S37 (Secondary) |
| url | https://arxiv.org/abs/2505.16907 |