On asymptotic Assouad–Nagata dimension
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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 $\dim(��_L X)$ 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.
28 pages, 0 figures
- University of Florida United States
- University of Florida United States
51F99; 54F45, Assouad–Nagata dimension, Metric Geometry (math.MG), Geometric Topology (math.GT), Higson corona, 54F45, Mathematics - Geometric Topology, 51F99, Mathematics - Metric Geometry, primary, FOS: Mathematics, Asymptotic dimension, Geometry and Topology, secondary, Dimension
51F99; 54F45, Assouad–Nagata dimension, Metric Geometry (math.MG), Geometric Topology (math.GT), Higson corona, 54F45, Mathematics - Geometric Topology, 51F99, Mathematics - Metric Geometry, primary, FOS: Mathematics, Asymptotic dimension, Geometry and Topology, secondary, Dimension
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