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Helly complexes are Hellyfications of their boundaries

  • Martín Blufstein
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Abstract

We prove that every finite Helly complex is isomorphic, at the level of its $1$-skeleton, to the Hellyfication (equivalently, the discrete injective hull) of its combinatorial boundary equipped with the metric induced from the complex. In particular, the boundary-rigidity phenomenon for Helly complexes proved by Blufstein-Chalopin-Chepoi admits a canonical injective-hull interpretation, independent of reconstruction procedures based on dismantling.

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Cite

BibTeXRIS
BibTeX
@misc{blufstein2026helly,
  title = {{Helly complexes are Hellyfications of their boundaries}},
  author = {Martín Blufstein},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21067},
  eprint = {2609.21067},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21067},
}
RIS
TY  - UNPB
TI  - Helly complexes are Hellyfications of their boundaries
AU  - Martín Blufstein
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.21067
UR  - https://arxiv.org/abs/2609.21067
AB  - We prove that every finite Helly complex is isomorphic, at the level of its $1$-skeleton, to the Hellyfication (equivalently, the discrete injective hull) of its combinatorial boundary equipped with the metric induced from the complex. In particular, the boundary-rigidity phenomenon for Helly complexes proved by Blufstein-Chalopin-Chepoi admits a canonical injective-hull interpretation, independent of reconstruction procedures based on dismantling.
ER  -