Universal minimal flows relative to a URS

Let G be a locally compact group and let Sub(G) denote the compact space of closed subgroups of G. G acts naturally on Sub (G) by conjugation. A uniformly recurrent subgroup (URS) of G is a closed, minimal subset of Sub (G). To every minimal topological dynamical system of G one can naturally associate its stabilizer URS and Glasner and Weiss asked whether every URS can be obtained in this manner. We answer this question in the affirmative by constructing, for a fixed URS H, a G-flow with stabilizer URS equal to H and universal for all minimal flows whose stabilizer URS is subordinate to H. This is joint work with Nicolas Matte Bon.Non UBCUnreviewedAuthor affiliation: Université Paris 7Facult