Géométries modèles de dimension trois
On expose une preuve détaillée de la classification par Thurston des huit géométries modèles de dimension trois.
Geometry of compactifications of locally symmetric spaces
For a locally symmetric space , we define a compactification which we call the “geodesic compactification”. It is constructed by adding limit points in to certain geodesics in . The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give for locally symmetric spaces. Moreover, has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in...
Gromov's measure equivalence and rigidity of higher rank lattices.
Group cohomology and the singularities of the Selberg zeta function associated to a Kleinian group.
Group Cohomology with Lipschitz Control and Higher Signatures.
Groupes de Ping-Pong et comptage
Dans cet article, nous étudions les propriétés asymptotiques d’une large classe de sous-groupe discrets du groupe linéaire réel : les groupes de Ping-Pong. Nous décrivons leur action sur l’espace projectif réel et le comportement à l’infini de leur fonction de comptage.
Groupes de Schottky et comptage
Soient un espace symétrique de type non compact et un groupe discret d’isométries de du type de Schottky. Dans cet article, nous donnons des équivalents des fonctions orbitales de comptage pour l’action de sur .
Groups acting on trees : from local to global structure
Group-theoretic compactification of Bruhat–Tits buildings
Harmonic maps and representations of non-uniform lattices of
We study representations of lattices of into . We show that if a representation is reductive and if is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic -space to complex hyperbolic -space. This allows us to give a differential geometric proof of rigidity results obtained by M. Burger and A. Iozzi. We also define a new invariant associated to representations into of non-uniform lattices in , and more generally of fundamental groups of orientable...
Harmonic maps into singular spaces and -adic superrigidity for lattices in groups of rank one
Holomorphic actions, Kummer examples, and Zimmer program
We classify compact Kähler manifolds of dimension on which acts a lattice of an almost simple real Lie group of rank . This provides a new line in the so-called Zimmer program, and characterizes certain complex tori as compact Kähler manifolds with large automorphisms groups.
Holomorphy of Eisenstein series at special points and cohomology of arithmetic subgroups of SLn (Q).
How frequent are discrete cyclic subgroups of semisimple Lie groups?
Hyperbolic 4-manifolds and conformally flat 3-manifolds
Hyperbolic 4-manifolds and tesselations
Hyperbolic geometry and moduli of real cubic surfaces
Let be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimensional geodesic subspaces from a real hyperbolic space and form the quotient by an arithmetic group to obtain an orbifold isomorphic to a component of the moduli space. There are five components. For each we describe the corresponding lattices in . We also derive several new and several old results on the topology of ....
Indefinite quadratic forms and unipotent flows on homogeneous spaces
Integral quadratic forms : applications to algebraic geometry
Intersections in hyperbolic manifolds.