Boundary rigidity of finite CAT(0) cube complexes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909709529776128 |
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| author | Chalopin, Jérémie Chepoi, Victor |
| author_facet | Chalopin, Jérémie Chepoi, Victor |
| contents | In this note, we prove that finite CAT(0) cube complexes can be reconstructed from their boundary distances (computed in their 1-skeleta). This result was conjectured by Haslegrave, Scott, Tamitegama, and Tan (2023). The reconstruction of a finite cell complex from the boundary distances is the discrete version of the boundary rigidity problem, which is a classical problem from Riemannian geometry. In the proofs, we use the bijection between CAT(0) cube complexes and median graphs and the corner peelings of median graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_04223 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Boundary rigidity of finite CAT(0) cube complexes Chalopin, Jérémie Chepoi, Victor Combinatorics Discrete Mathematics In this note, we prove that finite CAT(0) cube complexes can be reconstructed from their boundary distances (computed in their 1-skeleta). This result was conjectured by Haslegrave, Scott, Tamitegama, and Tan (2023). The reconstruction of a finite cell complex from the boundary distances is the discrete version of the boundary rigidity problem, which is a classical problem from Riemannian geometry. In the proofs, we use the bijection between CAT(0) cube complexes and median graphs and the corner peelings of median graphs. |
| title | Boundary rigidity of finite CAT(0) cube complexes |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2310.04223 |