Fixed points in compactifications and combinatorial counterparts
[Points fixes dans les compactifications et contreparties combinatoires]
Annales Henri Lebesgue, Tome 2 (2019), pp. 149-185.

La correspondance de Kechris–Pestov–Todorcevic établit une relation entre la moyennabilité extrême des groupes topologiques et les propriétés de type Ramsey de certaines classes de structures finies. Le but de cet article est de la resituer comme une instance particulière d’une construction plus générale, permettant ainsi de montrer que des énoncés de type Ramsey apparaissent en fait comme l’expression combinatoire naturelle de l’existence de points fixes dans certaines compactifications de groupes, et que des correspondances similaires sont en réalité présentes dans toute une variété de contextes dynamiques.

The Kechris–Pestov–Todorcevic correspondence connects extreme amenability of topological groups with Ramsey properties of classes of finite structures. The purpose of the present paper is to recast it as one of the instances of a more general construction, allowing to show that Ramsey-type statements actually appear as natural combinatorial expressions of the existence of fixed points in certain compactifications of groups, and that similar correspondences in fact exist in various dynamical contexts.

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DOI : https://doi.org/10.5802/ahl.16
Classification : 37B05,  03C15,  03E02,  05D10,  22F50,  43A07,  54H20
Mots clés : Ramsey theory, fixed point properties in topological dynamics
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Nguyen Van Thé, Lionel. Fixed points in compactifications and combinatorial counterparts. Annales Henri Lebesgue, Tome 2 (2019), pp. 149-185. doi : 10.5802/ahl.16. http://archive.numdam.org/articles/10.5802/ahl.16/

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