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Article Dans Une Revue Scientiae Mathematicae Japonicae Année : 2015

On relative extreme amenability

Résumé

The purpose of this paper is to study the notion of relative extreme amenability for pairs of topological groups. We give a characterization by a fixed point property on universal spaces. In addition we introduce the concepts of an extremely amenable interpolant as well as maximally relatively extremely amenable pairs and give examples. It is shown that relative extreme amenability does not imply the existence of an extremely amenable interpolant. The theory is applied to generalize results of Kechris, Pestov and Todorcevic relating to the application of Fra\"{i}ssé theory to the theory of Dynamical Systems. In particular, new conditions enabling to characterize universal minimal spaces of automorphism groups of Fra\"{i}ssé structures are given.

Dates et versions

hal-00662487 , version 1 (24-01-2012)

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Citer

Yonatan Gutman, Lionel Nguyen van Thé. On relative extreme amenability. Scientiae Mathematicae Japonicae, 2015, 28. ⟨hal-00662487⟩
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