2023/10/06 by Chalopin, Jérémie, Chepoi, Victor
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2310.04223
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.