English

Decomposition complexity growth of finitely generated groups

Group Theory 2019-02-26 v2 Metric Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.1902.08561,
  title  = {Decomposition complexity growth of finitely generated groups},
  author = {Trevor Davila},
  journal= {arXiv preprint arXiv:1902.08561},
  year   = {2019}
}
R2 v1 2026-06-23T07:48:22.360Z