On Asymptotic Assouad-Nagata Dimension

Details On Asymptotic Assouad-Nagata Dimension On Asymptotic Assouad-Nagata Dimension

2006-07-06

arxiv.org/abs/math/0607143v1

Mathematics

Metric Geometry

28 pages, 0 figures

Scientific paper

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 $\dim(\nu_L X)$ 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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