Assuad-Nagata dimension of nilpotent groups with arbitrary left invariant metrics

J. Higes

paper

Assuad-Nagata dimension of nilpotent groups with arbitrary left invariant metrics

arXiv:0804.4533

Abstract

Suppose $G$ is a countable, not necessarily finitely generated, group. We show $G$ admits a proper, left-invariant metric $d_{G}$ such that the Assouad-Nagata dimension of $(G, d_{G})$ is infinite, provided the center of $G$ is not locally finite. As a corollary we solve two problems of A.Dranishnikov.

9 pages