2019/02/22 by Trevor Davila, Davila, Trevor
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1902.08561
openalex publication_date 2019/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Finite decomposition complexity and asymptotic dimension growth are two generalizations of M. Gromov's asymptotic dimension which can be used to prove property A for large classes of finitely generated groups of infinite asymptotic dimension. In this paper, we introduce the notion of decomposition complexity growth, which is a quasi-isometry invariant generalizing both finite decomposition complexity and dimension growth. We show that subexponential decomposition complexity growth implies property A, and is preserved by certain group and metric constructions.