Poincaré Duality for Generalized Persistence Diagrams of (co)Filtrations
arxiv(2022)
摘要
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.
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