Asymptotic dimension, Property A, and Lipschitz maps
Metric Geometry
2019-11-18 v1 Geometric Topology
Abstract
It is well-known that a paracompact space X is of covering dimension n if and only if any map f from X to a simplicial complex K can be pushed into its n-skeleton. We use the same idea to define dimension in the coarse category. It turns out the analog of maps f from X to K is related to asymptotically Lipschitz maps, the analog of paracompact spaces are spaces related to Yu's Property A, and the dimension coincides with Gromov's asymptotic dimension.
Cite
@article{arxiv.0909.4095,
title = {Asymptotic dimension, Property A, and Lipschitz maps},
author = {M. Cencelj and J. Dydak and A. Vavpetic},
journal= {arXiv preprint arXiv:0909.4095},
year = {2019}
}
Comments
10 pages