A Polish AR-Space with no Nontrivial Isotopy
The Polish space Y constructed in [vM1] admits no nontrivial isotopy. Yet, there exists a Polish group that acts transitively on Y.
Actions of large semigroups and random walks on isometric extensions of boundaries
Characterizing weakly symmetric spaces as Gelfand pairs.
Equivariant higher -theory for compact Lie group actions.
Finite orbit decomposition of real flag manifolds
Let be a connected real semi-simple Lie group and a closed connected subgroup. Let be a minimal parabolic subgroup of . It is shown that has an open orbit on the flag manifold if and only if it has finitely many orbits on . This confirms a conjecture by T. Matsuki.
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.
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.
Multicontact vector fields on Hessenberg manifolds.
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 observable subgroups of complex analytic groups and algebraic structures on analytic homogeneous spaces.
Preferred parameterisations on homogeneous curves
We show how to specify preferred parameterisations on a homogeneous curve in an arbitrary homogeneous space. We apply these results to limit the natural parameters on distinguished curves in parabolic geometries.
Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite riemannian metric
For a riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the riemannian exponential...
Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric
For a Riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the Riemannian exponential...
Reductive homogeneous spaces and nonassociative algebras
The purpose of these survey notes is to give a presentation of a classical theorem of Nomizu [Nom54] that relates the invariant affine connections on reductive homogeneous spaces and nonassociative algebras.
Tempered reductive homogeneous spaces
Let be a semisimple algebraic Lie group and a reductive subgroup. We find geometrically the best even integer for which the representation of in is almost . As an application, we give a criterion which detects whether this representation is tempered.
Vanishing of the first reduced cohomology with values in an -representation
We prove that the first reduced cohomology with values in a mixing -representation, , vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced -cohomology. As a byproduct, we prove a conjecture by Pansu. Namely, the first reduced -cohomology on homogeneous, closed at infinity, Riemannian manifolds vanishes. We also...
Vitesse dans le théorème limite central pour certains systèmes dynamiques quasi-hyperboliques
Nous présentons une méthode permettant d’établir le théorème limite central avec vitesse en pour certains systèmes dynamiques. Elle est basée sur une propriété de décorrélation forte qui semble assez naturelle dans le cadre des systèmes quasi-hyperboliques. Nous prouvons que cette propriété est satisfaite par les exemples des flots diagonaux sur un quotient compact de et les « transformations » non uniformément hyperboliques du tore étudiées par Shub et Wilkinson.