Geometric Obstructions in Finsler Spaces and Torsion-Free Persistent Homology
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911340111593472 |
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| author | Cavalcanti, Rafael |
| author_facet | Cavalcanti, Rafael |
| contents | We relate the novel concept of Topological Data Analysis in Finsler space with representability property, which is a natural obstruction to prevent spurious features in high dimensions. We use decomposition of integer matrix in order to find suitable prime integer $p$ such that persistent homology module over $\mathbb{Z}_p$ encompasses only the holes associated to the free part, in agreement with the rational case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22079 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric Obstructions in Finsler Spaces and Torsion-Free Persistent Homology Cavalcanti, Rafael Algebraic Topology We relate the novel concept of Topological Data Analysis in Finsler space with representability property, which is a natural obstruction to prevent spurious features in high dimensions. We use decomposition of integer matrix in order to find suitable prime integer $p$ such that persistent homology module over $\mathbb{Z}_p$ encompasses only the holes associated to the free part, in agreement with the rational case. |
| title | Geometric Obstructions in Finsler Spaces and Torsion-Free Persistent Homology |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2512.22079 |