Asymptotic cones and Assouad-Nagata dimension
Metric Geometry
2008-12-15 v3 Geometric Topology
Abstract
We prove the dimension of any asymptotic cone over a metric space X does not exceed the asymptotic Assouad-Nagata dimension of X. This improves a result of Dranishnikov and Smith who showed that dim(Y) does not exceed asymptotic Assouad-Nagata dimension of X for all separable subsets Y of special asymptotic cones of X over an exponential ultrafilter. We also show that Assouad-Nagata dimension of the discrete Heisenberg group equals its asymptotic dimension.
Keywords
Cite
@article{arxiv.math/0610338,
title = {Asymptotic cones and Assouad-Nagata dimension},
author = {J. Dydak and J. Higes},
journal= {arXiv preprint arXiv:math/0610338},
year = {2008}
}
Comments
11 pages, comments from Behrstock, Brodskiy, Dranishnikov included