An isometry theorem for persistent homology of circle-valued functions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915321704611840 |
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| author | Broomhead, Nathan Pirashvili, Mariam |
| author_facet | Broomhead, Nathan Pirashvili, Mariam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02999 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An isometry theorem for persistent homology of circle-valued functions Broomhead, Nathan Pirashvili, Mariam Algebraic Topology Representation Theory 55N31, 16G20, 16G70 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. |
| title | An isometry theorem for persistent homology of circle-valued functions |
| topic | Algebraic Topology Representation Theory 55N31, 16G20, 16G70 |
| url | https://arxiv.org/abs/2506.02999 |