Kaleidoscopic groups and the generic point property
Gianluca Basso, Université Lyon 1
Duchesne, Monod and Wesolek described how to associate to each permutation group of countable degree a group acting on a certain one-dimensional tree-like continuum. This is called its kaleidoscopic group. We reframe the construction in terms of countable structures and determine which dynamical properties are preserved when passing to the kaleidoscopic group. This requires a novel structural Ramsey theorem and produces a new class of examples exhibiting a poorly understood phenomenon, namely non-metrizable universal minimal flows with a comeager orbit.
This is joint work with Todor Tsankov.