Corpus ID: 235435740

Property (T) for Roelcke precompact Polish groups (after Ibarluc\'ia, building on work of Ben Yaacov and Tsankov)

  title={Property (T) for Roelcke precompact Polish groups (after Ibarluc\'ia, building on work of Ben Yaacov and Tsankov)},
  author={F. L. Maitre},
Née au début des années 2000 dans les travaux de Ben Yaacov, Berenstein, Henson et Usvyatsov (2008), la théorie des modèles métrique, ou théorie des modèles continue, permet d’étendre des techniques issues de la théorie des modèles classique à de nouveaux objets issus de l’analyse. Dans ce texte, nous allons nous intéresser à une utilisation récente et remarquable de la théorie des modèles continue dans le cadre des groupes polonais : la preuve par Ibarlucía (2021) du fait que tout groupe… Expand


On a Roelcke-precompact Polish group that cannot act transitively on a complete metric space
We study when a continuous isometric action of a Polish group on a complete metric space is, or can be, transitive. Our main results consist of showing that for certain Polish groups, namely Aut* (μ)Expand
The dynamical hierarchy for Roelcke precompact Polish groups
We study several distinguished function algebras on a Polish group G, under the assumption that G is Roelcke precompact. We do this by means of the model-theoretic translation initiated by Ben YaacovExpand
The Group Aut (μ) is Roelcke Precompact
  • E. Glasner
  • Mathematics
  • Canadian Mathematical Bulletin
  • 2012
Abstract Following a similar result of Uspenskij on the unitary group of a separable Hilbert space, we show that, with respect to the lower (or Roelcke) uniform structure, the Polish groupExpand
Eberlein oligomorphic groups
We study the Fourier--Stieltjes algebra of Roelcke precompact, non-archimedean, Polish groups and give a model-theoretic description of the Hilbert compactification of these groups. We characterizeExpand
Some geometric and dynamical properties of the Urysohn space
Abstract This is a survey article about the geometry and dynamical properties of the Urysohn space. Most of the results presented here are part of the author's Ph.D. thesis and were published in theExpand
Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups
We investigate the automorphism groups of $\aleph_0$-categorical structures and prove that they are exactly the Roelcke precompact Polish groups. We show that the theory of a structure is stable ifExpand
The following groups are considered: the automorphism group of a Lebesgue measure space (with finite or -finite measure), groups of measurable functions with values in a Lie group, and diffeomorphismExpand
Unitary Representations of Oligomorphic Groups
We obtain a complete classification of the continuous unitary representations of oligomorphic permutation groups (those include the infinite permutation group S∞, the automorphism group of theExpand
The representation of σ-algebras
We know that every Boolean algebra is isomorphic to a field, whereas a complete Boolean algebra need not be isomorphic to a complete field (since, for instance, it need not be atomic). It is naturalExpand
Quasi finitely axiomatizable totally categorical theories
On demontre que toutes les theories presque fortement minimales totalement categoriques sont axiomatisables par un nombre fini d'axiomes et le schema d'infini