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2013 | OriginalPaper | Chapter

Universal Flows of Closed Subgroups of S ∞ and Relative Extreme Amenability

Author : L. Nguyen Van Thé

Published in: Asymptotic Geometric Analysis

Publisher: Springer New York

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Abstract

This paper is devoted to the study of universality for a particular continuous action naturally attached to certain pairs of closed subgroups of S ∞ . It shows that three new concepts, respectively called relative extreme amenability, relative Ramsey property for embeddings and relative Ramsey property for structures, are relevant in order to understand this property correctly. It also allows us to provide a partial answer to a question posed in [2] by Kechris, Pestov and Todorcevic (Geom. Funct. Anal. 15(1), 106–189, 2005).

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previous chapter A Remark on the Extremal Non-Central Sections of the Unit Cube
next chapter Oscillation of Urysohn Type Spaces
Literature
1.
Y. Gutman and L. Nguyen Van Thé, Relative extreme amenability and interpolation, preprint, 2011.
2.
A. S. Kechris, V. G Pestov, and S. Todorcevic, Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups, Geom. Funct. Anal. 15 (2005), no. 1, 106–189.
3.
L. Nguyen Van Thé, More on Kechris-Pestov-Todorcevic correspondence: precompact expansions, Fund. Math., accepted.
4.
L. Nguyen Van Thé, Structural Ramsey theory of metric spaces and topological dynamics of isometry groups, Mem. Amer. Math. Soc. 206 (2010), no. 968, x+140.
5.
V. G. Pestov, Ramsey-Milman phenomenon, Urysohn metric spaces, and extremely amenable groups, Israel J. Math. 127 (2002), 317–357.MathSciNetMATHCrossRef
6.
V. G. Pestov, Dynamics of infinite-dimensional groups, University Lecture Series, vol. 40, American Mathematical Society, Providence, RI, 2006, The Ramsey-Dvoretzky-Milman phenomenon, Revised edition of Dynamics of infinite-dimensional groups and Ramsey-type phenomena [Inst. Mat. Pura. Apl. (IMPA), Rio de Janeiro, 2005; MR2164572].
7.
M. Sokić, Ramsey properties of finite posets and related structures, Ph.D. thesis, University of Toronto, 2010.
8.
M. Sokić, Ramsey properties of finite posets, Order 29(2012), no. 1, 1–30.
9.
M. Sokić, Ramsey property, ultrametric spaces, finite posets, and universal minimal flows, preprint, 2011.
Metadata
Title
Universal Flows of Closed Subgroups of S ∞ and Relative Extreme Amenability
Author
L. Nguyen Van Thé
Copyright Year
2013
Publisher
Springer New York
Book
Asymptotic Geometric Analysis

Print ISBN: 978-1-4614-6405-1

Electronic ISBN: 978-1-4614-6406-8

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4614-6406-8_10

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