L-fuzzy simplicial homology
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911578479132672 |
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| author | Perera-Lago, Javier Torras-Casas, Alvaro Gonzalez-Diaz, Rocio |
| author_facet | Perera-Lago, Javier Torras-Casas, Alvaro Gonzalez-Diaz, Rocio |
| contents | Simplicial homology is a classical tool that assigns a sequence of modules to a simplicial complex, providing invariants for the study of its topological properties. In this article, we introduce the notion of L-fuzzy simplicial homology, a generalization of simplicial homology for L-fuzzy subcomplexes, in which each simplex is assigned a value from a completely distributive lattice L. We present its definition and main properties and describe methods to compute its structure. In addition, we interpret filtrations over a poset and chromatic datasets in this setting, opening a door to further applications in topological data analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08166 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | L-fuzzy simplicial homology Perera-Lago, Javier Torras-Casas, Alvaro Gonzalez-Diaz, Rocio Algebraic Topology Simplicial homology is a classical tool that assigns a sequence of modules to a simplicial complex, providing invariants for the study of its topological properties. In this article, we introduce the notion of L-fuzzy simplicial homology, a generalization of simplicial homology for L-fuzzy subcomplexes, in which each simplex is assigned a value from a completely distributive lattice L. We present its definition and main properties and describe methods to compute its structure. In addition, we interpret filtrations over a poset and chromatic datasets in this setting, opening a door to further applications in topological data analysis. |
| title | L-fuzzy simplicial homology |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2604.08166 |