2-Categorical Foundations for Multiparameter Persistence
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915426822258688 |
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| author | Angel, Mauricio |
| author_facet | Angel, Mauricio |
| contents | This paper introduces a novel approach to multi-parameter persistence using 2-categorical structures. We develop a framework that captures hierarchical interactions between filter parameters, overcoming fundamental limitations of traditional persistence modules. Our 2-categorical model yields new invariants that effectively characterize multidimensional topological features while maintaining computational tractability. We prove stability theorems for these invariants and demonstrate their effectiveness through applications in genomics and complex network analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02914 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 2-Categorical Foundations for Multiparameter Persistence Angel, Mauricio Algebraic Topology Differential Geometry 55N31, 18D05, 62R40 This paper introduces a novel approach to multi-parameter persistence using 2-categorical structures. We develop a framework that captures hierarchical interactions between filter parameters, overcoming fundamental limitations of traditional persistence modules. Our 2-categorical model yields new invariants that effectively characterize multidimensional topological features while maintaining computational tractability. We prove stability theorems for these invariants and demonstrate their effectiveness through applications in genomics and complex network analysis. |
| title | 2-Categorical Foundations for Multiparameter Persistence |
| topic | Algebraic Topology Differential Geometry 55N31, 18D05, 62R40 |
| url | https://arxiv.org/abs/2508.02914 |