Metrizable universal minimal flows of Polish groups have a comeagre orbit

Itaï Ben Yaacov (1) , Julien Melleray (1) , Todor Tsankov (2)

1 ICJ - Institut Camille Jordan
2 IMJ - Institut de Mathématiques de Jussieu

We prove that, whenever $G$ is a Polish group with metrizable universal minimal flow $M(G)$, there exists a comeagre orbit in $M(G)$. It then follows that there exists an extremely amenable, closed, co-precompact subgroup $G^*$ of $G$ such that $M(G)= \widehat{G/G^*}$.

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

Itaï Ben Yaacov, Julien Melleray, Todor Tsankov. Metrizable universal minimal flows of Polish groups have a comeagre orbit. 2016. ⟨hal-01266539v2⟩