Polyhedral CAT(0) metrics on locally finite complexes

Karim A. Adiprasito; Louis Funar

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arXiv · 2404.14878

Polyhedral CAT(0) metrics on locally finite complexes

Karim A. Adiprasito·Louis Funar

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Abstract

We prove the arborescence of any locally finite complex that is $CAT(0)$ with a polyhedral metric for which all vertex stars are convex. In particular locally finite $CAT(0)$ cube complexes or equilateral simplicial complexes are arborescent. Moreover, a triangulated manifold admits a $CAT(0)$ polyhedral metric if and only if it admits arborescent triangulations. We prove eventually that every locally finite complex which is $CAT(0)$ with a polyhedral metric has a barycentric subdivision which is arborescent.

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Karim A. Adiprasito, Louis Funar. 2024-04-23. Polyhedral CAT(0) metrics on locally finite complexes. https://arxiv.org/abs/2404.14878

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