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.
Cite
@article{arxiv.1902.08561,
title = {Decomposition complexity growth of finitely generated groups},
author = {Trevor Davila},
journal= {arXiv preprint arXiv:1902.08561},
year = {2019}
}