Poincaré Duality for Generalized Persistence Diagrams of (co)Filtrations

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 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.

Final version

References in corpus (1)

• Virtual persistence diagrams, signed measures, Wasserstein distances, and Banach spaces