Coarse amenability at infinity
Group Theory
2019-01-01 v1 Metric Geometry
Operator Algebras
Abstract
We define two different weakenings of coarse amenability (also known as Yu's property A), namely fibred coarse amenability and coarse amenability at infinity. These two properties allow us to prove that a residually finite group is coarsely amenable if and only if some (or all) of its box spaces satisfy the weak properties. We then elaborate on a result of Willett by showing that graphs with large girth always satisfy fibred coarse amenability. Finally, we discuss some examples and counter-examples to these properties.
Cite
@article{arxiv.1812.11745,
title = {Coarse amenability at infinity},
author = {Thibault Pillon},
journal= {arXiv preprint arXiv:1812.11745},
year = {2019}
}
Comments
12 pages