Amenability, Folner sets, and cooling functions

Details Amenability, Folner sets, and cooling functions Amenability, Folner sets, and cooling functions

2011-12-30

arxiv.org/abs/1201.0132v1

Mathematics

Group Theory

Scientific paper

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.

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