Persistent homology for functionals
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866913186116009984 |
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| author | Bauer, Ulrich Medina-Mardones, Anibal M. Schmahl, Maximilian |
| author_facet | Bauer, Ulrich Medina-Mardones, Anibal M. Schmahl, Maximilian |
| contents | We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence diagrams, which, in particular, implies that they satisfy generalized Morse inequalities. We illustrate the applicability of these results by recasting the original proof of the Unstable Minimal Surface Theorem given by Morse and Tompkins in a modern and rigorous framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_14247 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Persistent homology for functionals Bauer, Ulrich Medina-Mardones, Anibal M. Schmahl, Maximilian Algebraic Topology Functional Analysis 55N31, 58E05, 58E12, 54D05, 55N05 We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence diagrams, which, in particular, implies that they satisfy generalized Morse inequalities. We illustrate the applicability of these results by recasting the original proof of the Unstable Minimal Surface Theorem given by Morse and Tompkins in a modern and rigorous framework. |
| title | Persistent homology for functionals |
| topic | Algebraic Topology Functional Analysis 55N31, 58E05, 58E12, 54D05, 55N05 |
| url | https://arxiv.org/abs/2107.14247 |