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Poincaré duality for generalized persistence diagrams of (co)filtrations

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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 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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Acknowledgements

We thank Alex McCleary for providing the proof for Proposition 6.3. The first author thanks Primoz Skraba for hosting him at Queen Mary University London (2022–2023) and for the many insightful discussions on the Möbius inversion and persistent homology.

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  1. Department of Mathematics, Colorado State University, Fort Collins, USA

    Amit Patel & Tatum Rask

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  1. Amit Patel
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  2. Tatum Rask
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Correspondence to Amit Patel.

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This work is partially funded by the Leverhulme Trust Grant VP2-2021-008 awarded to the first author.

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Patel, A., Rask, T. Poincaré duality for generalized persistence diagrams of (co)filtrations. J Appl. and Comput. Topology (2024). https://doi.org/10.1007/s41468-023-00159-0

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  • DOI: https://doi.org/10.1007/s41468-023-00159-0

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