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arXiv · 2609.21067

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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Martín Blufstein. 2026-09-17. Helly complexes are Hellyfications of their boundaries. https://arxiv.org/abs/2609.21067

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