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Følner Functions and Geometry of Følner Sets in Groups

By Anna Ershler

Appears in collection : Representations, Probability, and Beyond : A Journey into Anatoly Vershik’s World

The definition of Følner function of groups is given in 1973 paper of A.M. Vershik, his appendix to the Russian translation of Greenleaf's book on amenable groups. We give of survey of the results about this asymptotic invariant of groups, properties of Følner sets in groups and discuss open questions in this domain.

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