Groupes de Cremona, connexité et simplicité
Le groupe de Cremona est connexe en toute dimension et, muni de sa topologie, il est simple en dimension .
Group-theoretic compactification of Bruhat–Tits buildings
Hilbert C*-modules and amenable actions
We study actions of discrete groups on Hilbert C*-modules induced from topological actions on compact Hausdorff spaces. We show non-amenability of actions of non-amenable and non-a-T-menable groups, provided there exists a quasi-invariant probability measure which is sufficiently close to being invariant.
Homogeneity rank of real representations of compact Lie groups.
Homogeneous deformations of discrete groups.
Homogeneous spaces of compact connected Lie groups which admit nontrivial invariant algebras.
Lie group structures on groups of diffeomorphisms and applications to CR manifolds
We give general sufficient conditions to guarantee that a given subgroup of the group of diffeomorphisms of a smooth or real-analytic manifold has a compatible Lie group structure. These results, together with recent work concerning jet parametrization and complete systems for CR automorphisms, are then applied to determine when the global CR automorphism group of a CR manifold is a Lie group in an appropriate topology.
Lifting smooth homotopies of orbit spaces of proper Lie group actions.
Meilleures approximations diophantiennes simultanées et théorème de Lévy
D'après le théorème de Lévy, les dénominateurs du développement en fraction continue d'un réel croissent presque sûrement à une vitesse au plus exponentielle. Nous étendons cette estimation aux meilleures approximations diophantiennes simultanées de formes linéaires.
Metric groups, unitary representations and continuous logic
We describe how properties of metric groups and of unitary representations of metric groups can be presented in continuous logic. In particular we find -axiomatization of amenability. We also show that in the case of locally compact groups some uniform version of the negation of Kazhdan’s property (T) can be viewed as a union of first-order axiomatizable classes. We will see when these properties are preserved under taking elementary substructures.
Minimal actions of homeomorphism groups
Let X be a closed manifold of dimension 2 or higher or the Hilbert cube. Following Uspenskij one can consider the action of Homeo(X) equipped with the compact-open topology on , the space of maximal chains in , equipped with the Vietoris topology. We show that if one restricts the action to M ⊂ Φ, the space of maximal chains of continua, then the action is minimal but not transitive. Thus one shows that the action of Homeo(X) on , the universal minimal space of Homeo(X), is not transitive (improving...
More on the Kechris-Pestov-Todorcevic correspondence: Precompact expansions
In 2005, the paper [KPT05] by Kechris, Pestov and Todorcevic provided a powerful tool to compute an invariant of topological groups known as the universal minimal flow. This immediately led to an explicit representation of this invariant in many concrete cases. However, in some particular situations, the framework of [KPT05] does not allow one to perform the computation directly, but only after a slight modification of the original argument. The purpose of the present paper is to supplement [KPT05]...
Multicontact vector fields on Hessenberg manifolds.
On a special class of Frobenius groups admitting planar partitions.
On countable dense and strong n-homogeneity
We prove that if a space X is countable dense homogeneous and no set of size n-1 separates it, then X is strongly n-homogeneous. Our main result is the construction of an example of a Polish space X that is strongly n-homogeneous for every n, but not countable dense homogeneous.
On derivations and crossed homomorphisms
We discuss some results about derivations and crossed homomorphisms arising in the context of locally compact groups and their group algebras, in particular, L¹(G), the von Neumann algebra VN(G) and actions of G on related algebras. We answer a question of Dales, Ghahramani, Grønbæk, showing that L¹(G) is always permanently weakly amenable. Then we show that for some classes of groups (e.g. IN-groups) the homology of L¹(G) with coefficients in VN(G) is trivial. But this is no longer true, in general,...
On extendability of invariant distributions
In this paper sufficient conditions are given in order that every distribution invariant under a Lie group extend from the set of orbits of maximal dimension to the whole of the space. It is shown that these conditions are satisfied for the n-point action of the pure Lorentz group and for a standard action of the Lorentz group of arbitrary signature.
On observable subgroups of complex analytic groups and algebraic structures on analytic homogeneous spaces.
On the algebraic structure of the unitary group.
We consider the unitary group U of complex, separable, infinite-dimensional Hilbert space as a discrete group. It is proved that, whenever U acts by isometries on a metric space, every orbit is bounded. Equivalently, U is not the union of a countable chain of proper subgroups, and whenever E ⊆ U generates U, it does so by words of a fixed finite length.
On the dynamics of isometries.