Corpus ID: 116001578

Sur la cohomologie et le spectre des vari et es localement sym etriques

  title={Sur la cohomologie et le spectre des vari et es localement sym etriques},
  author={N. Bergeron},
This volume is intended as an expository account of some re- sults and problems concerning the cohomology of locally symmetric spaces (especially arithmetic ones) and the relationship with the spectral theory of automorphic forms. The discussion is divided into four chapters: { A general introduction to arithmetic manifolds, Matsushima's formula and cohomological representations; { Cohomology of hyperbolic manifolds; { Isolation properties in the automorphic spectrum; { Cohomology of arithmetic… Expand
2 Citations
Benjamini-Schramm convergence of locally symmetric spaces
The main theme of this work is the study of geometry and topology of locally symmetric spaces Gamma\ X as ther volume Vol(\Gamma\ X) tends to infinity. Our first main result concerns theExpand
Strong limit multiplicity for arithmetic hyperbolic surfaces and 3-manifolds
We show that every sequence of torsion free arithmetic congruence lattices in ${\rm PGL}(2,\mathbb R)$ or ${\rm PGL}(2,\mathbb C)$ satisfies a strong quantitative version of the Limit MultiplicityExpand


Propriétés de Lefschetz dans la cohomologie de certaines variétés arithmétiques : le cas des surfaces modulaires de Hilbert
We first state new conjectures, of "Lefschetz type" on the relationships between the (co-)homology of arithmeticréai and complexhyperbolicmanifolds and the (co-) homology of their totaily geodesieExpand
Produits dans la cohomologie des varietes de Shimura : quelques calculs
Products in the cohomology of Shimura varieties: some calculations. We show how our recent results (arXiv:math.NT/0403407 v1 24 Mar 2004) together with a criterion of Venkataramana can be used to getExpand
Asymptotique de la norme $L^2$ d'un cycle géodésique dans les revêtements de congruence d'une variété hyperbolique arithmétique
Abstract. Let M be an arithmetic hyperbolic manifold and $F\subset M$ be a codimension 1 geodesic cycle. In this paper, we study the asymptotic growth of the $L^2$-norm of the lifts of F in theExpand
  • N. Bergeron
  • Mathematics
  • Journal of the Institute of Mathematics of Jussieu
  • 2007
Nous donnons une nouvelle démonstration d’un théorème de Vogan qui classifie les représentations cohomologiques isolées dans le dual unitaire d’un groupe de Lie semisimple réel. Nous étudions laExpand
Sur la $L^2$-cohomologie des variétés à courbure négative
We give a topological interpretation of the space of L2-harmonic forms on finite-volume manifolds with sufficiently pinched negative curvature. We give examples showing that this interpretation failsExpand
The notion of an /-geodesie cycle in a hyperbolic manifold generalises, in dimension /, that of a closed geodesie. In this note we study some topological of such cycles. Then we show that theExpand
Non-vanishing theorems for the cohomology of certain arithmetic quotients.
This paper is concerned with constructions of automorphic forms on classical groups. Our main tool is a very old one, namely that of theta series. Suppose (G, G') is a real reductive dual pair [14].Expand
Lefschetz properties for arithmetic real and complex hyperbolic manifolds
(Lefschetz theorem). The purpose of this paper is to point out an analogous, still mostly conjectural, result for arithmetic real and complex hyperbolic manifoldsM = Γ\X obtained as quotient of aExpand
On the first cohomology of arithmetic groups
Abstract: We study the restriction to smaller subgroups, of cohomology classes on arithmetic groups (possibly after moving the class by Hecke correspondences), especially in the context of firstExpand
L2-Cohomology and group cohomology
LETY be an arbitrary topological space and let I be a countable group which acts on Y. In this paper we study some homotopy theoretic invariants of such actions. In many respects, our treatmentExpand