On relative extreme amenability (Q2815612)

The paper under review deals with the problem of analyzing the notion of relative extreme amenability for pairs of topological groups. The authors present a characterization by a fixed point property on universal spaces. Moreover, the notions of an extremely amenable interpolant as well as maximally relatively extremely amenable pairs are introduced and motivated with interesting examples. It is shown that relative extreme amenability does not imply the existence of an extremely amenable interpolant. As an application the theory is applied to generalize results of [\textit{A. S. Kechris} et al., Geom. Funct. Anal. 15, No. 1, 106--189 (2005; Zbl 1084.54014)] relating to the application of Fraïssé theory to theory of Dynamical Systems. In particular, new conditions enabling to characterize universal minimal spaces of automorphism groups of Fraïssé structures are given.