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Trevor Davila

Publications and source records attributed to Trevor Davila.

2 recordsLinked to original sources
arXiv2019

Decomposition complexity growth of finitely generated groups

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.

math.GR↗
arXiv2016

On asymptotic property C

Asymptotic property C was introduced by Dranishnikov to study spaces with infinite asymptotic dimension. We show that asymptotic property C is preserved by infinite products. We also show that countable restricted direct products of countable groups with finite asymptotic dimension have asymptotic property C. Then we introduce hyperbolic property C, an infinite dimensional version of hyperbolic dimension.

math.GT↗