Simplifications of finite spaces equipped with sheaves
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912158391992320 |
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| author | Malko, Artem |
| author_facet | Malko, Artem |
| contents | Following the classical results of Stong, we introduce a cohomological analogue of a core of a finite sheaved topological space and propose an algorithm for simplification in this category. In particular we generalize the notion of beat vertices and show that if a vertex of a sheaved space has topologically acyclic downset (with trivial coefficients), then its removal preserves the sheaf cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11354 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simplifications of finite spaces equipped with sheaves Malko, Artem Algebraic Topology 55N30, 18B35, 55U10, 06A07 Following the classical results of Stong, we introduce a cohomological analogue of a core of a finite sheaved topological space and propose an algorithm for simplification in this category. In particular we generalize the notion of beat vertices and show that if a vertex of a sheaved space has topologically acyclic downset (with trivial coefficients), then its removal preserves the sheaf cohomology. |
| title | Simplifications of finite spaces equipped with sheaves |
| topic | Algebraic Topology 55N30, 18B35, 55U10, 06A07 |
| url | https://arxiv.org/abs/2412.11354 |