Discrete Differential Calculus on Simplicial Complexes and Constrained Homology
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866910939124596736 |
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| author | Ren, Shiquan |
| author_facet | Ren, Shiquan |
| contents | Let $V$ be a finite set. Let $\mathcal{K}$ be a simplicial complex with its vertices in $V$. In this paper, we discuss some differential calculus on $V$. We construct some constrained homology groups of $\mathcal{K}$ by using the differential calculus on $V$. Moreover, we define an independent hypergraph to be the complement of a simplicial complex in the complete hypergraph on $V$. Let $\mathcal{L}$ be an independent hypergraph with its vertices in $V$. We construct some constrained cohomology groups of $\mathcal{L}$ by using the differential calculus on $V$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_01452 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Discrete Differential Calculus on Simplicial Complexes and Constrained Homology Ren, Shiquan Algebraic Topology Primary 55U10, 55U15, Secondary 53A45, 08A50 Let $V$ be a finite set. Let $\mathcal{K}$ be a simplicial complex with its vertices in $V$. In this paper, we discuss some differential calculus on $V$. We construct some constrained homology groups of $\mathcal{K}$ by using the differential calculus on $V$. Moreover, we define an independent hypergraph to be the complement of a simplicial complex in the complete hypergraph on $V$. Let $\mathcal{L}$ be an independent hypergraph with its vertices in $V$. We construct some constrained cohomology groups of $\mathcal{L}$ by using the differential calculus on $V$. |
| title | Discrete Differential Calculus on Simplicial Complexes and Constrained Homology |
| topic | Algebraic Topology Primary 55U10, 55U15, Secondary 53A45, 08A50 |
| url | https://arxiv.org/abs/2104.01452 |