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arXiv · 2208.05243

Combinatorial Persistent Homology Transform

Brittany Terese Fasy·Amit Patel
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Abstract

The combinatorial interpretation of the persistence diagram as a M\"obius inversion was recently shown to be functorial. We employ this discovery to recast the Persistent Homology Transform of a geometric complex as a representation of a cellulation on $\mathbb{S}^n$ to the category of combinatorial persistence diagrams. Detailed examples are provided. We hope this recasting of the PH transform will allow for the adoption of existing methods from algebraic and topological combinatorics to the study of shapes.

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BibTeXRIS

Brittany Terese Fasy, Amit Patel. 2022-08-10. Combinatorial Persistent Homology Transform. https://doi.org/10.3934/fods.2024020

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