Poincaré Duality for Generalized Persistence Diagrams of (co)Filtrations

12/30/2022

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by   Amit Patel, et al.

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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.