Combinatorial Persistent Homology Transform
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866914796830457856 |
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| author | Fasy, Brittany Terese Patel, Amit |
| author_facet | Fasy, Brittany Terese Patel, Amit |
| contents | The combinatorial interpretation of the persistence diagram as a Möbius inversion was recently shown to be functorial. We employ this discovery to recast the Persistent Homology Transform of a geometric complex as a representation of a cellulation on $\mathbb{S}^n$ to the category of combinatorial persistence diagrams. Detailed examples are provided. We hope this recasting of the PH transform will allow for the adoption of existing methods from algebraic and topological combinatorics to the study of shapes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_05243 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Combinatorial Persistent Homology Transform Fasy, Brittany Terese Patel, Amit Algebraic Topology Computational Geometry Category Theory 55U99, 68P01, 57Z25 The combinatorial interpretation of the persistence diagram as a Möbius inversion was recently shown to be functorial. We employ this discovery to recast the Persistent Homology Transform of a geometric complex as a representation of a cellulation on $\mathbb{S}^n$ to the category of combinatorial persistence diagrams. Detailed examples are provided. We hope this recasting of the PH transform will allow for the adoption of existing methods from algebraic and topological combinatorics to the study of shapes. |
| title | Combinatorial Persistent Homology Transform |
| topic | Algebraic Topology Computational Geometry Category Theory 55U99, 68P01, 57Z25 |
| url | https://arxiv.org/abs/2208.05243 |