Sous-groupes discrets des groupes de Lie : rigidité, arithméticité

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1. [A] E. Andreev, Convex polyhedra of finite volume in Lobachevski space, Mat. Sb.83 (1970), 256-260. Zbl0203.54904MR273510
2. [A-B] N. A'Campo et M. Burger, Une preuve du théorème de superrigidité de G.A. Margulis, Preprint Université de Basel, (1991). 
3. [B-M-S] H. Bass, J. Milnor and J.-P. Serre, Solution of the congruence subgroup prob- 
4. lem for SLn (n ≥ 3) and Sp2n (n ≥ 2), Publ. Math. I. H. E. S.33 (1967), 59-137. 
5. [Bo] R. Borcherds, Automorphism groups of Lorentzian lattices, J. of Algebra111 (1987), 133-153. Zbl0628.20003MR913200
6. [B1] A. Borel, On the curvature tensor of the hermitian symmetric manifolds, Ann. of Math.71 (1960), 508-521. Zbl0100.36101MR111059
7. [B2] A. Borel, Compact Clifford-Klein forms of symmetric spaces, Topology2 (1963), 111-122. Zbl0116.38603MR146301
8. [B3] A. Borel, Introduction aux groupes arithmétiques, Hermann, Paris (1969). Zbl0186.33202MR244260
9. [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). Zbl0443.22010MR554917
10. [B-T] F. Bruhat et J. Tits, Groupes réductifs sur un corps local, Publ. Math. I. H. E. S.41 (1972), 5-252. Zbl0254.14017MR327923
11. [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. Zbl0129.14102MR133787
12. [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. Zbl0695.58010MR1019964
13. [C-V] E. Calabi and E. Vesentini, On compact locally symmetric Kähler manifolds, Ann. of Math.71 (1960), 472-507. Zbl0100.36002MR111058
14. [C-W] P. Cohen et J. Wolfart, Fonctions hypergéométriques en plusieurs variables et espaces de modules de variétés abéliennes, Ann. Sci. Ec. Norm. Sup. Paris26 (1993), 665-690. Zbl0822.14014MR1251148
15. [Co1] K. Corlette, Flat G-bundles with canonical metrics, J. Differen. Geom.28 (1988), 361-382. Zbl0676.58007MR965220
16. [Co2] K. Corlette, Archimedean superrigidity and hyperbolic geometry, Ann. of Math.135 (1992), 165-182. Zbl0768.53025MR1147961
17. [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). Zbl0214.04602
18. [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. Zbl0615.22008MR849651
19. [E-S] J. Eells and J. Sampson, Harmonic maps of Riemannian manifolds, Amer. J. Math.86 (1964), 109-160. Zbl0122.40102MR164306
20. [F] H. Furstenberg, Poisson boundaries and envelopes of discrete groups, Bull. Amer. Math. Soc.73 (1967), 350-356. Zbl0184.33105MR210812
21. [Ga1] H. Garland, A rigidity theorem for discrete subgroups, Trans. Amer. Math. Soc.129 (1967), 1-25. Zbl0225.22016MR214102
22. [Ga2] H. Garland, p-adic curvature and the cohomology of discrete subgroups of p-adic groups, Ann. of Math.97 (1973), 375-423. Zbl0262.22010MR320180
23. [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. Zbl0678.53059MR972343
24. [G1] M. Gromov, Hyperbolic groups, in "Essays in group theory", ed. S. Gersten, Springer Verlag, Heidelberg (1987), 75-265. Zbl0634.20015MR919829
25. [G2] M. Gromov, The foliated Plateau problem I, Geom. Functional Anal.1 (1992), 14-79 ; idem : II, ibidem253-320. Zbl0768.53012MR1091610
26. [G-P] M. Gromov and I. Piatetski-Shapiro, Non-arithmetic groups in Lobachevsky spaces, Publ. Math. I. H. E. S.66 (1988), 93-103. Zbl0649.22007MR932135
27. [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. Zbl0896.58024MR1215595
28. [H] N.J. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc.55 (1987), 59-126. Zbl0634.53045MR887284
29. [H-V] P. de la Harpe et P. Valette, La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque175, Soc. Math. de France (1989). Zbl0759.22001
30. [J-Y] J. Jost and S.T. Yau, Harmonic maps and superrigidity, Proc. Symp. Pure Math.54 (1993), 245-280. Zbl0806.58012MR1216587
31. [K-N] S. Kaneyuki and T. Nagano, On certain quadratic forms related to symmetric Riemannian spaces, Osaka Math. J.14 (1962), 241-252. Zbl0114.13403MR159347
32. [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). Zbl0857.57038MR1380646
33. [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. Zbl0168.27602MR209390
34. [Kh] A.G. Khovanski, Hyperplane section of polyhedra, toroidal manifolds and discrete groups in Lobatchevski space, Funkc. Anal. i Prilozh.20 (1986), 50-61. Zbl0597.51014MR831049
35. [La] F. Labourie, Existence d'applications harmoniques tordues à valeurs dans les variétés à courbure négative, Proc. Amer. Math. Soc.111 (1991), 877-882. Zbl0783.58016MR1049845
36. [Lu] A. Lubotsky, Trees and discrete subgroups of Lie groups over locla fields, Bull. Amer. Math. Soc.20 (1989), 27-30. Zbl0676.22007MR945301
37. [Ma1] G.A. Margulis, Discrete groups of motions of manifolds of nonpositive curvature, Amer. Math. Soc. Transl.109 (1977), 33-45. Zbl0367.57012MR492072
38. [Ma2] G.A. Margulis, Arithmeticity and finite dimensional representations of uni- form lattices, Funkc. Anal. i Prilozh.8 (1974), 258-259. Zbl0303.22005MR357689
39. [Ma3] G.A. Margulis, Discrete subgroups of semisimple Lie groups, Ergeb. der Math. Band 17, Springer Verlag, Berlin (1990). Zbl0732.22008MR1090825
40. [Mat] Y. Matsushima, On the first Betti number of compact quotient spaces of higher-dimensional symmetric spaces, Ann. of Math.75 (1962), 312-330. Zbl0118.38303MR158406
41. [Mok] N. Mok, Metric rigidity theorems on Hermitian locally symmetric manifolds, World Sci., Singapore (1989). Zbl0912.32026MR1081948
42. [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. Zbl0189.09402MR1055358
43. [M2] G.D. Mostow, The rigidity of locally symmetric spaces, Proc. Intern. Congress of Math. (1970), 187-197. Zbl0224.53028MR419683
44. [M3] G.D. Mostow, Strong rigidity of locally symmetric spaces, Annals of Math. Studies, Study 78, Princeton Univ. Press, Princeton N.J. (1973). Zbl0265.53039MR385004
45. [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. Zbl0605.22008MR837205
46. [M5] G.D. Mostow, Generalized Picard lattices arising from half-integral conditions., Publ. Math. I.H.E.S.63 (1986), 91-106. Zbl0615.22009MR849652
47. [M-S-Y] N. Mok, Y.T. Siu and S.K. Yeung, Geometric superrigidity, Invent. Math.113 (1993), 57-83. Zbl0808.53043MR1223224
48. [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. Nauk28 (1987), 401-411. Zbl0613.51010
49. [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). Zbl0765.20022
50. [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. Zbl0201.36603MR130324
51. [Sa] J. Sampson, Applications of harmonic maps to Kähler geometry, Contemp. Math.49 (1986), 125-133. Zbl0605.58019MR833809
52. [Si1] C. Simpson, Higgs bundles and local systems, Publ. Math. I. H. E. S.75 (1992), 5-95. Zbl0814.32003MR1179076
53. [Si2] C. Simpson, Integrality of rigid local systems of rank two on a smooth pro- jective variety, Preprint Université de Toulouse (1992). MR1179076
54. [Siu] Y.T. Siu, Complex analyticity of harmonic maps, and strong rigidity of compact Kähler manifolds, Ann. of Math.112 (1980), 73-111. Zbl0517.53058MR584075
55. [Th1] W. Thurston, The geometry and topology of 3-manifolds, Princeton University Press, Princeton (1978). 
56. [Th2] W. Thurston, Shape of polyhedra, Preprint Princeton Univ. (1987). 
57. [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 Zbl0238.20052MR224710
58. [T2] J. Tits, Lectures on buildings of spherical type and finite B-N pairs, Lecture Notes Band 386, Springer Verlag, Heidelberg (1970). Zbl0295.20047
59. [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). MR492073
60. [To] D. Toledo, Representations of surface groups in PSU(n,1) with maximum characteristic number, J. Differen. Geom.29 (1989), 125-134. Zbl0676.57012MR978081
61. [V] E.B. Vinberg, Geometry II, Encyclopedia of Math. Sci., Springer Verlag, Heidelberg, (1990). Zbl0786.00008
62. [W-Z] McK. Wang and W. Ziller, Symmetric spaces and strongly isotropy irreducible spaces, Preprint Univ. of Pennsylvania (1991). MR1219904
63. [W] A. Weil, On discrete subgroups of Lie groups II, Ann. of Math.75 (1962), 578-602. Zbl0131.26602MR137793
64. [Z] R. Zimmer, Ergodic theory and semisimple groups, Monographs in Math. vol. 81, Birkhäuser, Basel (1984). Zbl0571.58015MR776417
65. [Zuo] K. Zuo, Factorizations of nonrigid Zariski dense representations of π1 of projective algebraic manifolds, Preprint Universität Kaiserslautern (1991). 

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