Persistent Homology Transform Cosheaf

08/10/2022

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by   Brittany Terese Fasy, et al.

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We employ the recent discovery of functoriality for persistent homology to recast the Persistent Homology Transform of a geometric complex as a cosheaf of combinatorial persistence diagrams. Detailed examples are provided. We hope the recasting of the PH transform as a cellular cosheaf will allow for the adoption of existing methods from category theory and (co)sheaf theory to the study of shapes.