Polish groups with metrizable universal minimal flows

By Julien Melleray, L. N. V. Th'e, Todor Tsankov. 2014

50 citations recorded by the source corpus.

We prove that if the universal minimal flow of a Polish group $G$ is metrizable and contains a $G_\delta$ orbit $G \cdot x_0$, then it is isomorphic to the completion of the homogeneous space $G/G_{x_0}$ and show how this result translates naturally in terms of structural Ramsey theory. We also investigate universal minimal proximal flows and describe concrete representations of them in a number of examples.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c435b39d3355b3e81d296a16b86abe371d25e133

Citations in the corpus

• Metrizable universal minimal flows of Polish groups have a comeagre orbit (2016, unknown): “Then there exists a closed, co-precompact, extremely amenable subgroup Our proof is based on the recent work of Melleray, Nguyen Van Thé, and Tsankov [MNT 15 ], where the conclusion of Theorem 1 .”