Coarse structures on groups
Geometric Topology
2012-01-24 v1 Group Theory
Abstract
We introduce the group-compact coarse structure on a Hausdorff topological group in the context of coarse structures on an abstract group which are compatible with the group operations. We develop asymptotic dimension theory for the group-compact coarse structure generalizing several familiar results for discrete groups. We show that the asymptotic dimension in our sense of the free topological group on a non-empty topological space that is homeomorphic to a closed subspace of a Cartesian product of metrizable spaces is 1.
Cite
@article{arxiv.1201.4687,
title = {Coarse structures on groups},
author = {Andrew Nicas and David Rosenthal},
journal= {arXiv preprint arXiv:1201.4687},
year = {2012}
}