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arXiv · 2212.14610

Poincar\'e Duality for Generalized Persistence Diagrams of (co)Filtrations

Amit Patel·Tatum Rask
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Abstract

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 Poincar\'e 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.

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Amit Patel, Tatum Rask. 2022-12-30. Poincar\'e Duality for Generalized Persistence Diagrams of (co)Filtrations. https://doi.org/10.1007/s41468-023-00159-0

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