Fixed points in compactifications and combinatorial counterparts

Lionel Nguyen van Thé (1)

1 I2M - Institut de Mathématiques de Marseille

The Kechris-Pestov-Todorcevic correspondence connects extreme amenability of non-Archimedean Polish 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.

Mots clés: Ramsey theory; fixed point properties in topological dynamics

Domaines: Systèmes dynamiques [math.DS]; Combinatoire [math.CO]; Logique [math.LO]

Lionel Nguyen van Thé. Fixed points in compactifications and combinatorial counterparts. Annales Henri Lebesgue, 2019, 2. ⟨hal-01438243⟩