Cellular sheaf Laplacians on the set of simplices of symmetric simplicial set induced by hypergraph
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909388133892096 |
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| author | Choi, Seongjin Park, Junyeong |
| author_facet | Choi, Seongjin Park, Junyeong |
| contents | We generalize cellular sheaf Laplacians on an ordered finite abstract simplicial complex to the set of simplices of a symmetric simplicial set. We construct a functor from the category of hypergraphs to the category of finite symmetric simplicial sets and define cellular sheaf Laplacians on the set of simplices of finite symmetric simplicial set induced by hypergraph. We provide formulas for cellular sheaf Laplacians and show that cellular sheaf Laplacian on an ordered finite abstract simplicial complex is exactly the ordered cellular sheaf Laplacian on the set of simplices induced by abstract simplicial complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08458 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cellular sheaf Laplacians on the set of simplices of symmetric simplicial set induced by hypergraph Choi, Seongjin Park, Junyeong Algebraic Topology 55U10, 55N05, 55N30 We generalize cellular sheaf Laplacians on an ordered finite abstract simplicial complex to the set of simplices of a symmetric simplicial set. We construct a functor from the category of hypergraphs to the category of finite symmetric simplicial sets and define cellular sheaf Laplacians on the set of simplices of finite symmetric simplicial set induced by hypergraph. We provide formulas for cellular sheaf Laplacians and show that cellular sheaf Laplacian on an ordered finite abstract simplicial complex is exactly the ordered cellular sheaf Laplacian on the set of simplices induced by abstract simplicial complex. |
| title | Cellular sheaf Laplacians on the set of simplices of symmetric simplicial set induced by hypergraph |
| topic | Algebraic Topology 55U10, 55N05, 55N30 |
| url | https://arxiv.org/abs/2411.08458 |