On Asymptotic Assouad-Nagata Dimension
| dc.creator | Dranishnikov, A. N. | |
| dc.creator | Smith, J. | |
| dc.date | 2006-07-06 | |
| dc.date.accessioned | 2026-07-07T07:18:05Z | |
| dc.date.available | 2026-07-07T07:18:05Z | |
| dc.description | 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. | |
| dc.description | 28 pages, 0 figures | |
| dc.identifier | https://arxiv.org/abs/math/0607143 | |
| dc.identifier | http://arxiv.org/abs/math/0607143 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114173 | |
| dc.subject | Metric Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 51F99; 54F45 | |
| dc.title | On Asymptotic Assouad-Nagata Dimension | |
| dc.type | text |