Ergodic theory, semisimple Lie groups and foliations by manifolds of negative curvature
Publications Mathématiques de l'IHÉS, Tome 55 (1982), pp. 37-62. 
@article{PMIHES_1982__55__37_0,
     author = {Zimmer, Robert J.},
     title = {Ergodic theory, semisimple {Lie} groups and foliations by manifolds of negative curvature},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {37--62},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {55},
     year = {1982},
     mrnumber = {672181},
     zbl = {0525.57022},
     language = {en},
     url = {http://archive.numdam.org/item/PMIHES_1982__55__37_0/}
}
TY  - JOUR
AU  - Zimmer, Robert J.
TI  - Ergodic theory, semisimple Lie groups and foliations by manifolds of negative curvature
JO  - Publications Mathématiques de l'IHÉS
PY  - 1982
SP  - 37
EP  - 62
VL  - 55
PB  - Institut des Hautes Études Scientifiques
UR  - http://archive.numdam.org/item/PMIHES_1982__55__37_0/
LA  - en
ID  - PMIHES_1982__55__37_0
ER  - 
%0 Journal Article
%A Zimmer, Robert J.
%T Ergodic theory, semisimple Lie groups and foliations by manifolds of negative curvature
%J Publications Mathématiques de l'IHÉS
%D 1982
%P 37-62
%V 55
%I Institut des Hautes Études Scientifiques
%U http://archive.numdam.org/item/PMIHES_1982__55__37_0/
%G en
%F PMIHES_1982__55__37_0
Zimmer, Robert J. Ergodic theory, semisimple Lie groups and foliations by manifolds of negative curvature. Publications Mathématiques de l'IHÉS, Tome 55 (1982), pp. 37-62. http://archive.numdam.org/item/PMIHES_1982__55__37_0/

[1] M. Berger, P. Gauduchon, E. Mazet, Le spectre d'une variété Riemannienne, Lecture Notes in Math., No. 194, New York, Springer-Verlag, 1971. | MR | Zbl

[2] R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1-49. | MR | Zbl

[3] A. Borel and J.-P. Serre, Corners and arithmetic groups, Comm. Math. Helv., 48 (1973), 436-491. | MR | Zbl

[4] A. Connes, J. Feldman, B. Weiss, Amenable equivalence relations are generated by a single transformation, preprint. | Zbl

[5] P. Eberlein, B. O'Neill, Visibility manifolds, Pacific J. Math., 46 (1973), 45-109. | MR | Zbl

[6] P. Eberlein, Geodesic flows on negatively curved manifolds, I, Annals of Math., 95 (1972), 492-510. | MR | Zbl

[7] P. Eberlein, Geodesic flows on negatively curved manifolds, II, Trans. Amer. Math. Soc., 178 (1973), 57-82. | MR | Zbl

[8] P. Eberlein, Busemann functions are C2, unpublished.

[9] J. Feldman, C. C. Moore, Ergodic equivalence relations, cohomology, and von Neumann algebras, I, Trans. Amer. Math. Soc., 234 (1977), 289-324. | MR | Zbl

[10] J. Feldman, P. Hahn, C. C. Moore, Orbit structure and countable sections for actions of continuous groups, Adv. in Math., 28 (1978), 186-230. | MR | Zbl

[11] H. Furstenberg, A Poisson formula for semisimple Lie groups, Annals of Math., 77 (1963), 335-383. | MR | Zbl

[12] P. Halmos, Ergodic Theory, New York, Chelsea, 1956. | MR | Zbl

[13] E. Heintze, H.-C. Imhof, Geometry of horospheres, J. Diff. Geom., 12 (1977), 481-491. | MR | Zbl

[14] M. Hirsch, W. Thurston, Foliated bundles, invariant measures, and flat manifolds, Annals of Math., 101 (1975), 369-390. | MR | Zbl

[15] R. Kallman, Certain quotient spaces are countably separated, III, J. Funct. Anal., 22 (1976), 225-241. | MR | Zbl

[16] G. W. Mackey, Borel structures in groups and their duals, Trans. Amer. Math. Soc., 85 (1957), 134-165. | MR | Zbl

[17] G. W. Mackey, Point realizations of transformation groups, Ill. J. Math., 6 (1962), 327-335. | MR | Zbl

[18] G. W. Mackey, Ergodic theory and virtual groups, Math. Ann., 166 (1966), 187-207. | MR | Zbl

[19] G. A. Margulis, Discrete groups of motions of manifolds of non-positive curvature, Amer. Math. Soc. Translations, 109 (1977), 33-45. | Zbl

[20] G. A. Margulis, Factor groups of discrete subgroups, Soviet Math. Dokl., 19 (1978), 1145-1149. | Zbl

[21] G. A. Margulis, Quotient groups of discrete subgroups and measure theory, Funct. Anal. Appl., 12 (1978), 295-305. | MR | Zbl

[22] C. C. Moore, Compactifications of symmetric spaces, Amer. J. Math., 86 (1964), 201-218. | MR | Zbl

[23] C. C. Moore, Ergodicity of flows on homogeneous spaces, Amer. J. Math., 88 (1966), 154-178. | MR | Zbl

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

[25] G. D. Mostow, Strong rigidity of locally symmetric spaces, Annals of Math. Studies, No. 78, Princeton University Press, 1973. | MR | Zbl

[26] D. Ornstein, B. Weiss, Ergodic Theory of amenable group actions, I, Bull. Amer. Math. Soc., 2 (1980), 161. | MR | Zbl

[27] A. Ramsay, Virtual groups and group actions, Adv. in Math., 6 (1971), 253-322. | MR | Zbl

[28] D. Ruelle, D. Sullivan, Currents, flows, and diffeomorphisms, Topology, 14 (1975), 319-327. | MR | Zbl

[29] I. Satake, On representations and compactifications of symmetric Riemannian spaces, Annals of Math., 71 (1960), 77-110. | MR | Zbl

[30] C. Series, Foliations of polynomial growth are hyperfinite, Israel J. Math., 34 (1979), 245-258. | MR | Zbl

[31] R. J. Zimmer, Amenable ergodic group actions and an application to Poisson boundaries of random walks, J. Funct. Anal., 27 (1978), 350-372. | MR | Zbl

[32] R. J. Zimmer, Hyperfinite factors and amenable ergodic actions, Invent. Math., 41 (1977), 23-31. | MR | Zbl

[33] R. J. Zimmer, Induced and amenable ergodic actions of Lie groups, Ann. Sci. Ec. Norm. Sup., 11 (1978), 407-428. | Numdam | MR | Zbl

[34] R. J. Zimmer, Orbit spaces of unitary representations, ergodic theory, and simple Lie groups, Annals of Math., 106 (1977), 573-588. | MR | Zbl

[35] R. J. Zimmer, Algebraic topology of ergodic Lie group actions and measurable foliations, preprint.

[36] R. J. Zimmer, Strong rigidity for ergodic actions of semisimple Lie groups, Annals of Math., 112 (1980), 511-529. | MR | Zbl

[37] R. J. Zimmer, Orbit equivalence and rigidity of ergodic actions of Lie groups, Ergodic Theory and Dynamical Systems, 1 (1981), 237-253. | MR | Zbl

[38] R. J. Zimmer, On the Mostow rigidity theorem and measurable foliations by hyperbolic space, Israel J. Math., to appear. | Zbl

[39] R. J. Zimmer, Curvature of leaves of amenable foliations, American J. Math., to appear. | Zbl

[40] D. Anosov, Ya. Sinai, Some smooth ergodic systems, Russian Math. Surveys, 22 (1967), 103-67. | Zbl

[41] P. Eberlein, Lattices in spaces of nonpositive curvature, Annals of Math., 111 (1980), 435-467. | MR | Zbl