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arXiv · 2506.13219

Boundary rigidity of systolic and Helly complexes

Martín Blufstein·Jérémie Chalopin·Victor Chepoi
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Abstract

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.

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Martín Blufstein, Jérémie Chalopin, Victor Chepoi. 2025-06-16. Boundary rigidity of systolic and Helly complexes. https://arxiv.org/abs/2506.13219

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