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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.16416 |
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| _version_ | 1866910056168030208 |
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| author | Leśkiewicz, Jakub Furmanek, Bartosz Lipiński, Michał Morozov, Dmitriy |
| author_facet | Leśkiewicz, Jakub Furmanek, Bartosz Lipiński, Michał Morozov, Dmitriy |
| contents | Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some persistent homological features, without affecting the rest. We present a new approach to simplification based on the concept of forbidden regions and combinatorial dynamics. It allows us to reorder and cancel critical values, whose cancellation is not possible using existing methods because they are not consecutive in the total order. Each such cancellation takes O(c$\cdot$n) time in the worst case, where c is the number of birth-death pairs and n is the size of the input complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16416 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological simplification guided by forbidden regions Leśkiewicz, Jakub Furmanek, Bartosz Lipiński, Michał Morozov, Dmitriy Algebraic Topology 55N31 Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some persistent homological features, without affecting the rest. We present a new approach to simplification based on the concept of forbidden regions and combinatorial dynamics. It allows us to reorder and cancel critical values, whose cancellation is not possible using existing methods because they are not consecutive in the total order. Each such cancellation takes O(c$\cdot$n) time in the worst case, where c is the number of birth-death pairs and n is the size of the input complex. |
| title | Topological simplification guided by forbidden regions |
| topic | Algebraic Topology 55N31 |
| url | https://arxiv.org/abs/2603.16416 |