Amenability, Folner sets, and cooling functions
Group Theory
2012-01-04 v1
Abstract
Erling Folner proved that the amenability or nonamenability of a countable group depends on the complexity of its finite subsets. Complexity has three measures: maximum Folner ratio, optimal cooling function, and minimum cooling norm. Our first aim is to show that, for a fixed finite subset, these three measures are tightly bound to one another. We then explore their algorithmic calculation. Our intent is to provide a theoretical background for algorithmically exploring the amenability and nonamenability of discrete groups.
Keywords
Cite
@article{arxiv.1201.0132,
title = {Amenability, Folner sets, and cooling functions},
author = {J. W. Cannon and W. J. Floyd and W. R. Parry},
journal= {arXiv preprint arXiv:1201.0132},
year = {2012}
}