Boundary rigidity of finite CAT(0) cube complexes
Combinatorics
2025-07-30 v2 Discrete Mathematics
Abstract
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.
Cite
@article{arxiv.2310.04223,
title = {Boundary rigidity of finite CAT(0) cube complexes},
author = {Jérémie Chalopin and Victor Chepoi},
journal= {arXiv preprint arXiv:2310.04223},
year = {2025}
}