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| Discrete Differential Calculus on Simplicial Complexes and Constrained Homology* |
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Citation： |
Shiquan REN.Discrete Differential Calculus on Simplicial Complexes and Constrained Homology*[J].Chinese Annals of Mathematics B,2023,44(4):615~640 |
| Page view： 1268
Net amount： 665 |
Authors： |
Shiquan REN; |
Foundation： |
This work was supported by China Postdoctoral Science Foundation (No. 2022M721023). |
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| Abstract： |
Let V be a finite set. Let K be a simplicial complex with its vertices in V .In this paper, the author discusses some differential calculus on V . He constructs some constrained homology groups of K by using the differential calculus on V . Moreover, he defines an independence hypergraph to be the complement of a simplicial complex in the complete hypergraph on V . Let L be an independence hypergraph with its vertices in V .He constructs some constrained cohomology groups of L by using the differential calculus on V . |
Keywords： |
Simplicial complexes, Hypergraphs, Chain complexes, Homology,Differential calculus |
Classification： |
55U10, 55U15, 53A45, 08A50 |
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