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Amenability of groups and \(G\)-sets. (English) Zbl 1490.43001

Berthé, Valérie (ed.) et al., Sequences, groups, and number theory. Cham: Birkhäuser. Trends Math., 433-544 (2018).
Summary: This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of Göttingen and the École Normale Supérieure. The goals of the text are (1) to be as self-contained as possible, so as to serve as a good introduction for newcomers to the field; (2) to stress the use of combinatorial tools, in collaboration with functional analysis, probability, etc., with discrete groups in focus; (3) to consider from the beginning the more general notion of amenable actions; and (4) to describe recent classes of examples and in particular groups acting on Cantor sets and topological full groups.
For the entire collection see [Zbl 1394.05002].

MSC:

43A07 Means on groups, semigroups, etc.; amenable groups
20E22 Extensions, wreath products, and other compositions of groups
20-02 Research exposition (monographs, survey articles) pertaining to group theory
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References:

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