2016/12/31 by Goulnara Arzhantseva, Graham A. Niblo, Graham Niblo +2
Mathematics · #Advanced Operator Algebra Research #Characterization (materials science) #Cube (algebra) #Dimension (graph theory) #Effective dimension #Geodesic #Geometric and Algebraic Topology #Geometry and complex manifolds #Minkowski–Bouligand dimension #Packing dimension #Rank (graph theory) #math.GR #math.MG #msc:20F65 #msc:20F67 #msc:20F69 #msc:51F99
paper · pdf · doi:10.2140/agt.2018.18.493
published as Algebr. Geom. Topol. 18 (2018) 493-524
arxiv created 2017/01/06 · openalex created_date 2017/01/26 · openalex publication_date 2018/01/10 · arxiv updated 2018/03/16 · openalex updated_date 2026/08/05
We give a characterization for asymptotic dimension growth. We apply it to [math] cube complexes of finite dimension, giving an alternative proof of Wright’s result on their finite asymptotic dimension. We also apply our new characterization to geodesic coarse median spaces of finite rank and establish that they have subexponential asymptotic dimension growth. This strengthens a recent result of S̆pakula and Wright.