Growth of the asymptotic dimension function for groups

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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.
14 pages, no figures

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Group Theory, Primary: 20F69, Secondary 20E06, 20E22, 20F65

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http://salesiana.dossiersoluciones.com/handle/123456789/75034

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0504577
 http://arxiv.org/abs/math/0504577

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arXiv