Sous-groupes discrets des groupes de Lie : rigidité, arithméticité
Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Exposé no. 778, 37 p.
@incollection{SB_1993-1994__36__69_0,
     author = {Pansu, Pierre},
     title = {Sous-groupes discrets des groupes de {Lie} : rigidit\'e, arithm\'eticit\'e},
     booktitle = {S\'eminaire Bourbaki : volume 1993/94, expos\'es 775-789},
     series = {Ast\'erisque},
     note = {talk:778},
     pages = {69--105},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {227},
     year = {1995},
     mrnumber = {1321644},
     zbl = {0835.22011},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1993-1994__36__69_0/}
}
TY  - CHAP
AU  - Pansu, Pierre
TI  - Sous-groupes discrets des groupes de Lie : rigidité, arithméticité
BT  - Séminaire Bourbaki : volume 1993/94, exposés 775-789
AU  - Collectif
T3  - Astérisque
N1  - talk:778
PY  - 1995
SP  - 69
EP  - 105
IS  - 227
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/SB_1993-1994__36__69_0/
LA  - fr
ID  - SB_1993-1994__36__69_0
ER  - 
%0 Book Section
%A Pansu, Pierre
%T Sous-groupes discrets des groupes de Lie : rigidité, arithméticité
%B Séminaire Bourbaki : volume 1993/94, exposés 775-789
%A Collectif
%S Astérisque
%Z talk:778
%D 1995
%P 69-105
%N 227
%I Société mathématique de France
%U http://www.numdam.org/item/SB_1993-1994__36__69_0/
%G fr
%F SB_1993-1994__36__69_0
Pansu, Pierre. Sous-groupes discrets des groupes de Lie : rigidité, arithméticité, dans Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Exposé no. 778, 37 p. http://www.numdam.org/item/SB_1993-1994__36__69_0/

[A] E. Andreev, Convex polyhedra of finite volume in Lobachevski space, Mat. Sb. 83 (1970), 256-260. | MR | Zbl

[A-B] N. A'Campo et M. Burger, Une preuve du théorème de superrigidité de G.A. Margulis, Preprint Université de Basel, (1991).

[B-M-S] H. Bass, J. Milnor and J.-P. Serre, Solution of the congruence subgroup prob-

lem for SLn (n ≥ 3) and Sp2n (n ≥ 2), Publ. Math. I. H. E. S. 33 (1967), 59-137. | DOI

[Bo] R. Borcherds, Automorphism groups of Lorentzian lattices, J. of Algebra 111 (1987), 133-153. | DOI | MR | Zbl

[B1] A. Borel, On the curvature tensor of the hermitian symmetric manifolds, Ann. of Math. 71 (1960), 508-521. | DOI | MR | Zbl

[B2] A. Borel, Compact Clifford-Klein forms of symmetric spaces, Topology 2 (1963), 111-122. | DOI | MR | Zbl

[B3] A. Borel, Introduction aux groupes arithmétiques, Hermann, Paris (1969). | MR | Zbl

[B-W] A. Borel and N. Wallach, Continuous cohomology, discrete subgroups and representations of reductive groups, Ann. Math. Studies, Princeton University Press, Princeton, N.J. (1980). | MR | Zbl

[B-T] F. Bruhat et J. Tits, Groupes réductifs sur un corps local, Publ. Math. I. H. E. S. 41 (1972), 5-252. | DOI | EuDML | Numdam | MR | Zbl

[C] E. Calabi, On compact Riemannian manifolds with constant curvature I, in "Differential Geometry", Proc. Symp. Pure Math. 3, Amer. Math. Soc., Providence, R.I. (1961), 155-180. | DOI | MR | Zbl

[C-T] J. Carlson and D. Toledo, Harmonic mappings of Kähler manifolds to locally symmetric spaces, Publ. Math. I.H.E.S. 69 (1989), 173-201. | DOI | EuDML | Numdam | MR | Zbl

[C-V] E. Calabi and E. Vesentini, On compact locally symmetric Kähler manifolds, Ann. of Math. 71 (1960), 472-507. | DOI | MR | Zbl

[C-W] P. Cohen et J. Wolfart, Fonctions hypergéométriques en plusieurs variables et espaces de modules de variétés abéliennes, Ann. Sci. Ec. Norm. Sup. Paris 26 (1993), 665-690. | DOI | EuDML | Numdam | MR | Zbl

[Co1] K. Corlette, Flat G-bundles with canonical metrics, J. Differen. Geom. 28 (1988), 361-382. | DOI | MR | Zbl

[Co2] K. Corlette, Archimedean superrigidity and hyperbolic geometry, Ann. of Math. 135 (1992), 165-182. | DOI | MR | Zbl

[D-K] C. Delaroche et A. Kirillov, Sur les relations entre l'espace dual d'un groupe et la structure de ses sous-groupes fermés, Séminaire Bourbaki, Exposé n° 343, (1967-68), Benjamin, New York (1969). | EuDML | Numdam | Zbl

[D-M] P. Deligne and G. D. Mostow, Monodromy of hypergeometric functions and non lattice integral monodromy, Publ. Math. I.H.E.S. 63 (1986), 5-89. | DOI | EuDML | Numdam | MR | Zbl

[E-S] J. Eells and J. Sampson, Harmonic maps of Riemannian manifolds, Amer. J. Math. 86 (1964), 109-160. | DOI | MR | Zbl

[F] H. Furstenberg, Poisson boundaries and envelopes of discrete groups, Bull. Amer. Math. Soc. 73 (1967), 350-356. | DOI | MR | Zbl

[Ga1] H. Garland, A rigidity theorem for discrete subgroups, Trans. Amer. Math. Soc. 129 (1967), 1-25. | DOI | MR | Zbl

[Ga2] H. Garland, p-adic curvature and the cohomology of discrete subgroups of p-adic groups, Ann. of Math. 97 (1973), 375-423. | DOI | MR | Zbl

[G-M] W. Goldman and J. Millson, The deformation theory of representations of fundamental groups of compact Kähler manifolds, Publ. Math. I.H.E.S. 67 (1988), 43-96. | DOI | EuDML | Numdam | MR | Zbl

[G1] M. Gromov, Hyperbolic groups, in "Essays in group theory", ed. S. Gersten, Springer Verlag, Heidelberg (1987), 75-265. | MR | Zbl

[G2] M. Gromov, The foliated Plateau problem I, Geom. Functional Anal. 1 (1992), 14-79 ; idem : II, ibidem 253-320. | DOI | EuDML | MR | Zbl

[G-P] M. Gromov and I. Piatetski-Shapiro, Non-arithmetic groups in Lobachevsky spaces, Publ. Math. I. H. E. S. 66 (1988), 93-103. | DOI | EuDML | Numdam | MR | Zbl

[G-S] M. Gromov and R. Schoen, Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one, Publ. Math. I.H.E.S. 76 (1992), 165-246. | DOI | EuDML | Numdam | MR | Zbl

[H] N. J. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55 (1987), 59-126. | DOI | MR | Zbl

[H-V] P. De La Harpe et P. Valette, La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque 175, Soc. Math. de France (1989). | Numdam | Zbl

[J-Y] J. Jost and S. T. Yau, Harmonic maps and superrigidity, Proc. Symp. Pure Math. 54 (1993), 245-280. | DOI | MR | Zbl

[K-N] S. Kaneyuki and T. Nagano, On certain quadratic forms related to symmetric Riemannian spaces, Osaka Math. J. 14 (1962), 241-252. | MR | Zbl

[K-L] A. Katok and J. Lewis, Global rigidity results for lattice actions on tori and new examples of volume preserving actions, Preprint Pennsylvania State University (1991). | MR | Zbl

[K] D. Kazhdan, Connection of the dual space of a group with the structure of its closed subgroups, Funkc. Anal. i Prilozh. 67 (1967), 71-74. | MR | Zbl

[Kh] A. G. Khovanski, Hyperplane section of polyhedra, toroidal manifolds and discrete groups in Lobatchevski space, Funkc. Anal. i Prilozh. 20 (1986), 50-61. | MR | Zbl

[La] F. Labourie, Existence d'applications harmoniques tordues à valeurs dans les variétés à courbure négative, Proc. Amer. Math. Soc. 111 (1991), 877-882. | MR | Zbl

[Lu] A. Lubotsky, Trees and discrete subgroups of Lie groups over local fields, Bull. Amer. Math. Soc. 20 (1989), 27-30. | DOI | MR | Zbl

[Ma1] G. A. Margulis, Discrete groups of motions of manifolds of nonpositive curvature, Amer. Math. Soc. Transl. 109 (1977), 33-45. | MR | Zbl

[Ma2] G. A. Margulis, Arithmeticity and finite dimensional representations of uniform lattices, Funkc. Anal. i Prilozh. 8 (1974), 258-259. | DOI | MR | Zbl

[Ma3] G. A. Margulis, Discrete subgroups of semisimple Lie groups, Ergeb. der Math. Band 17, Springer Verlag, Berlin (1990). | MR | Zbl

[Mat] Y. Matsushima, On the first Betti number of compact quotient spaces of higher-dimensional symmetric spaces, Ann. of Math. 75 (1962), 312-330. | DOI | MR | Zbl

[Mok] N. Mok, Metric rigidity theorems on Hermitian locally symmetric manifolds, World Sci., Singapore (1989). | MR | Zbl

[M1] G. D. Mostow, Quasiconformal mappings in n-space and the rigidity of hyperbolic space forms, Publ. Math. I.H.E.S. 34 (1967), 53-104. | DOI | EuDML | Numdam | MR | Zbl

[M2] G. D. Mostow, The rigidity of locally symmetric spaces, Proc. Intern. Congress of Math. (1970), 187-197. | MR | Zbl

[M3] G. D. Mostow, Strong rigidity of locally symmetric spaces, Annals of Math. Studies, Study 78, Princeton Univ. Press, Princeton N.J. (1973). | MR | Zbl

[M4] G. D. Mostow, Discrete subgroups of Lie groups, in "Elie Cartan et les Mathématiques d'aujourd'hui", Astérisque, numéro hors série (1985), 289-309. | Numdam | MR | Zbl

[M5] G. D. Mostow, Generalized Picard lattices arising from half-integral conditions., Publ. Math. I.H.E.S. 63 (1986), 91-106. | DOI | EuDML | Numdam | MR | Zbl

[M-S-Y] N. Mok, Y. T. Siu and S. K. Yeung, Geometric superrigidity, Invent. Math. 113 (1993), 57-83. | DOI | EuDML | MR | Zbl

[Pr] M. N. Prokhorov, The absence of discrete reflexion groups with noncompact fundamental polyhedron of finite volume in Lobachevsky space of large dimension, Izvest. Mat. Nauk 28 (1987), 401-411. | DOI | Zbl

[Ru] O. P. Ruzmanov, Examples of nonarithmetic crystallographic Coxeter groups in n-dimensional Lobachevsky space for 6 ≤ n ≤ 10, Problems in group theory and homological algebra (1989). | Zbl

[S] A. Selberg, On discontinuous groups in higher dimensional symmetric spaces, in "Intern. Coll. on Function Theory", Tata Institute of Fund. Research, Bombay, (1960), 147-164. | MR | Zbl

[Sa] J. Sampson, Applications of harmonic maps to Kähler geometry, Contemp. Math. 49 (1986), 125-133. | DOI | MR | Zbl

[Si1] C. Simpson, Higgs bundles and local systems, Publ. Math. I. H. E. S. 75 (1992), 5-95. | DOI | EuDML | Numdam | MR | Zbl

[Si2] C. Simpson, Integrality of rigid local systems of rank two on a smooth pro- jective variety, Preprint Université de Toulouse (1992). | MR

[Siu] Y. T. Siu, Complex analyticity of harmonic maps, and strong rigidity of compact Kähler manifolds, Ann. of Math. 112 (1980), 73-111. | DOI | MR | Zbl

[Th1] W. Thurston, The geometry and topology of 3-manifolds, Princeton University Press, Princeton (1978).

[Th2] W. Thurston, Shape of polyhedra, Preprint Princeton Univ. (1987).

[T1] J. Tits, Classification of algebraic groups, in "Algebraic groups and discrete subgroups", Proc. Symp. Pure Math., Amer. Math. Soc., Providence, R.I., 9 (1966), 33-62 | DOI | MR | Zbl

[T2] J. Tits, Lectures on buildings of spherical type and finite B-N pairs, Lecture Notes Band 386, Springer Verlag, Heidelberg (1970). | Zbl

[T3] J. Tits, Sur les travaux de Margulis, Séminaire Bourbaki, Exposé n° 482, (1975-76), Lect. Notes in Math. Vol 567, Springer Verlag, Berlin (1976). | Numdam | MR

[To] D. Toledo, Representations of surface groups in PSU(n,1) with maximum characteristic number, J. Differen. Geom. 29 (1989), 125-134. | MR | Zbl

[V] E. B. Vinberg, Geometry II, Encyclopedia of Math. Sci., Springer Verlag, Heidelberg, (1990). | Zbl

[W-Z] Mck. Wang and W. Ziller, Symmetric spaces and strongly isotropy irreducible spaces, Preprint Univ. of Pennsylvania (1991). | MR | Zbl

[W] A. Weil, On discrete subgroups of Lie groups II, Ann. of Math. 75 (1962), 578-602. | DOI | MR | Zbl

[Z] R. Zimmer, Ergodic theory and semisimple groups, Monographs in Math. vol. 81, Birkhäuser, Basel (1984). | MR | Zbl

[Zuo] K. Zuo, Factorizations of nonrigid Zariski dense representations of π1 of projective algebraic manifolds, Preprint Universität Kaiserslautern (1991). | Zbl