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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.01792 |
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| _version_ | 1866908477105897472 |
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| author | Boutry, Nicolas |
| author_facet | Boutry, Nicolas |
| contents | In this paper, we study some relationships existing between some particular mathematical structures: discrete surfaces coming from discrete topology and mathematical morphology, poset-based connected manifolds coming from discrete topology, and normal pseudomanifolds which are much used in discrete geometry and topological data analysis. We will also show that, even when poset-based connected manifolds are assumed to be simplicial complexes, and then supplied with many additional topological properties, they are not necessarily smooth. A set of sufficient conditions to ensure that poset-based connected manifolds are smooth will be provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01792 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong relations between discrete surfaces, poset-based connected manifolds, and normal pseudomanifolds Boutry, Nicolas Algebraic Topology In this paper, we study some relationships existing between some particular mathematical structures: discrete surfaces coming from discrete topology and mathematical morphology, poset-based connected manifolds coming from discrete topology, and normal pseudomanifolds which are much used in discrete geometry and topological data analysis. We will also show that, even when poset-based connected manifolds are assumed to be simplicial complexes, and then supplied with many additional topological properties, they are not necessarily smooth. A set of sufficient conditions to ensure that poset-based connected manifolds are smooth will be provided. |
| title | Strong relations between discrete surfaces, poset-based connected manifolds, and normal pseudomanifolds |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2508.01792 |