Relative extreme amenability and interpolation

Details Relative extreme amenability and interpolation Relative extreme amenability and interpolation

2011-05-31

arxiv.org/abs/1105.6221v2

Mathematics

Group Theory

21 pages. Last section reshaped and enriched with a new result that answers a question of the previous version of the paper

Scientific paper

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 in general, but that it does for a class of closed subgroups of the permutation group of the integers, naturally arising in Fra\"iss\'e Theory.

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