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arXiv · 1404.0421

On Asymptotic Dimension With Linear Control

Corry Bedwell
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Abstract

We construct a countable p-local group with a proper invariant metric whose Assouad-Nagata dimension is strictly greater than the asymptotic dimension with linear control. This solves Problem 8.6 from the list [Dr]. We study asymptotic dimension with linear control $\ell$-$asdim_{\omega}$ that depends on a fixed ultrafilter on the naturals. It turns out that the Assouad-Nagata dimension is the supremum of $\ell$-$asdim_{\omega}$ on all $\omega$ and the asymptotic dimension with linear control is the minimum.

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Corry Bedwell. 2014-04-02. On Asymptotic Dimension With Linear Control. https://doi.org/10.1016/j.topol.2014.05.006

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