Algebraic aspects of amenability

Jeudi 9 juin 2011 14:00-15:00 - Grigorchuk Rostyslav - Texas A&M University

Résumé : The notion of amenable group (under a different name) was> introduced in the case of discrete groups by J. von Neumann in 1929 and in> the more general setting of topological groups by N.N. Bogolyubov in 1939.> After that it started to play a fundamental role in many areas of> mathematics including Topology and Dynamical systems. Despite a lot of> activity in the study of amenable groups and their applications, and> of dozens> of completely different versions of the definition of amenability, for a long> period the algebraic structure of the class of amenable groups and their> algebraic properties was unclear.> > In my talk, I will give a survey of known results about the algebraic aspects> of amenability including such topics as : elementary amenability,> subexponential amenability (or « good groups » in terminology of M. Freedman> and P. Teichner), the Munhausen trick, various classes of groups of> type NF (no free subgroup on two generators), the amenable groups of branch> type, and finally the construction due to K. Medynets and speaker of> uncountably many finitely generated infinite amenable simple groups, which> is based on the use of minimal Cantor systems.> A number of open problems will be formulated during the talk.

Lieu : bât. 425 - 121-123

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