METRIZABLE UNIVERSAL MINIMAL FLOWS OF POLISH GROUPS HAVE A COMEAGRE ORBIT

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

1 AGL - Algèbre, géométrie, logique
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

Domains: Logic [math.LO]; Dynamical Systems [math.DS]

Itaï Ben Yaacov, Julien Melleray, Todor Tsankov. METRIZABLE UNIVERSAL MINIMAL FLOWS OF POLISH GROUPS HAVE A COMEAGRE ORBIT. Geometric And Functional Analysis, 2017, 27 (1), pp.67--77. ⟨hal-01266539v3⟩