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Growth of the asymptotic dimension function for groups

Gregory C. Bell
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Abstract

It is relatively easy to construct a finitely generated group with infinite asymptotic dimension: the restricted wreath product of $\mathbb{Z}$ by $\mathbb{Z}$ provides an example. In light of this, it becomes interesting to consider the rate of growth of the asymptotic dimension function of a group. Loosely speaking, we measure the dimension on $λ$-scale and let $λ$ increase to infinity to recover the asymptotic dimension. In this paper we consider how the asymptotic dimension function is affected by different constructions involving groups.

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Gregory C. Bell. 2005-04-28. Growth of the asymptotic dimension function for groups. https://arxiv.org/abs/math/0504577

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