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math.AT2022
Poincaré Duality for Generalized Persistence Diagrams of (co)Filtrations
Amit Patel, Tatum Rask
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 dualit…
math.AT2022★ 2 cited
Combinatorial Persistent Homology Transform
Brittany Terese Fasy, Amit Patel
The combinatorial interpretation of the persistence diagram as a Möbius inversion was recently shown to be functorial. We employ this discovery to recast the Persistent Homology Tr…