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On Asymptotic Assouad-Nagata Dimension

A. N. Dranishnikov·J. Smith
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Abstract

For a large class of metric space X including discrete groups we prove that the asymptotic Assouad-Nagata dimension AN-asdim X of X coincides with the covering dimension $\dim(ν_L X)$ of the Higson corona of X with respect to the sublinear coarse structure on X. Then we apply this fact to prove the equality AN-asdim(X x R) = AN-asdim X + 1. We note that the similar equality for Gromov's asymptotic dimension asdim generally fails to hold [Dr3]. Additionally we construct an injective map from the asymptotic cone without the basepoint to the sublinear Higson Corona.

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BibTeXRIS

A. N. Dranishnikov, J. Smith. 2006-07-06. On Asymptotic Assouad-Nagata Dimension. https://arxiv.org/abs/math/0607143

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