English

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.

Keywords

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

R2 v1 2026-06-21T13:49:18.169Z