Poincaré Duality for Generalized Persistence Diagrams of (co)Filtrations
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909162491871232 |
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| author | Patel, Amit Rask, Tatum |
| author_facet | Patel, Amit Rask, Tatum |
| contents | We dualize previous work on generalized persistence diagrams for filtrations to cofiltrations. When the underlying space is a manifold, we express this duality as a Poincaré duality between their generalized persistence diagrams. A heavy emphasis is placed on the recent discovery of functoriality of the generalized persistence diagram and its connection to Rota's Galois Connection Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_14610 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Poincaré Duality for Generalized Persistence Diagrams of (co)Filtrations Patel, Amit Rask, Tatum Algebraic Topology Computational Geometry Category Theory We dualize previous work on generalized persistence diagrams for filtrations to cofiltrations. When the underlying space is a manifold, we express this duality as a Poincaré duality between their generalized persistence diagrams. A heavy emphasis is placed on the recent discovery of functoriality of the generalized persistence diagram and its connection to Rota's Galois Connection Theorem. |
| title | Poincaré Duality for Generalized Persistence Diagrams of (co)Filtrations |
| topic | Algebraic Topology Computational Geometry Category Theory |
| url | https://arxiv.org/abs/2212.14610 |