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arXiv · 1902.08561

Decomposition complexity growth of finitely generated groups

Trevor Davila
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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.

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Trevor Davila. 2019-02-22. Decomposition complexity growth of finitely generated groups. https://arxiv.org/abs/1902.08561

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