Boundary rigidity of systolic and Helly complexes
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912828470853632 |
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| author | Blufstein, Martín Chalopin, Jérémie Chepoi, Victor |
| author_facet | Blufstein, Martín Chalopin, Jérémie Chepoi, Victor |
| contents | In this article, we prove that finite (weakly) systolic and Helly complexes can be reconstructed from their boundary distances (computed in their 1-skeleta). Furthermore, Helly complexes and 2-dimensional systolic complexes can be reconstructed by an algorithm that runs in polynomial time with respect to the number of vertices of the complex. Both results can be viewed as a positive contribution to a general question of Haslegrave, Scott, Tamitegama, and Tan (2025). The reconstruction of a finite cell complex from the boundary distances is the discrete analogue of the boundary rigidity problem, which is a classical problem from Riemannian geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13219 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary rigidity of systolic and Helly complexes Blufstein, Martín Chalopin, Jérémie Chepoi, Victor Combinatorics Group Theory Metric Geometry 51F99, 05C99, 52C99, 20F65 In this article, we prove that finite (weakly) systolic and Helly complexes can be reconstructed from their boundary distances (computed in their 1-skeleta). Furthermore, Helly complexes and 2-dimensional systolic complexes can be reconstructed by an algorithm that runs in polynomial time with respect to the number of vertices of the complex. Both results can be viewed as a positive contribution to a general question of Haslegrave, Scott, Tamitegama, and Tan (2025). The reconstruction of a finite cell complex from the boundary distances is the discrete analogue of the boundary rigidity problem, which is a classical problem from Riemannian geometry. |
| title | Boundary rigidity of systolic and Helly complexes |
| topic | Combinatorics Group Theory Metric Geometry 51F99, 05C99, 52C99, 20F65 |
| url | https://arxiv.org/abs/2506.13219 |