Polyhedral CAT(0) metrics on locally finite complexes

Autor:	Adiprasito, Karim A., Funar, Louis
Rok vydání:	2024
Předmět:	Mathematics - Geometric Topology Mathematics - Combinatorics 57N16 51K10 57N15
Druh dokumentu:	Working Paper
Popis:	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. Comment: 16p
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.14878 Zobrazit plný text záznamu View this record from Arxiv