An isometry theorem for persistent homology of circle-valued functions

Nathan Broomhead; Mariam Pirashvili

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arXiv · 2506.02999

An isometry theorem for persistent homology of circle-valued functions

Nathan Broomhead·Mariam Pirashvili

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Abstract

This paper explores persistence modules for circle-valued functions, presenting a new extension of the interleaving and bottleneck distances in this setting. We propose a natural generalisation of barcodes in terms of arcs on a geometric model associated to the derived category of quiver representations. The main result is an isometry theorem that establishes an equivalence between the interleaving distance and the bottleneck distance for circle-valued persistence modules.

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Nathan Broomhead, Mariam Pirashvili. 2025-06-03. An isometry theorem for persistent homology of circle-valued functions. https://arxiv.org/abs/2506.02999

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