@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},
volume = {56},
year = {1982},
pages = {37-62},
mrnumber = {84h:22022},
zbl = {0525.57022},
language = {en},
url = {http://dml.mathdoc.fr/item/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 56 (1982) pp. 37-62. http://gdmltest.u-ga.fr/item/PMIHES_1982__55__37_0/
[1] , , , Le spectre d'une variété Riemannienne, Lecture Notes in Math., No. 194, New York, Springer-Verlag, 1971. | MR 43 #8025 | Zbl 0223.53034
[2] and , Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1-49. | MR 40 #4891 | Zbl 0191.52002
[3] and , Corners and arithmetic groups, Comm. Math. Helv., 48 (1973), 436-491. | MR 52 #8337 | Zbl 0274.22011
[4] , , , Amenable equivalence relations are generated by a single transformation, preprint. | Zbl 0491.28018
[5] , , Visibility manifolds, Pacific J. Math., 46 (1973), 45-109. | MR 49 #1421 | Zbl 0264.53026
[6] , Geodesic flows on negatively curved manifolds, I, Annals of Math., 95 (1972), 492-510. | MR 46 #10024 | Zbl 0217.47304
[7] , Geodesic flows on negatively curved manifolds, II, Trans. Amer. Math. Soc., 178 (1973), 57-82. | MR 47 #2636 | Zbl 0264.53027
[8] , Busemann functions are C2, unpublished.
[9] , , Ergodic equivalence relations, cohomology, and von Neumann algebras, I, Trans. Amer. Math. Soc., 234 (1977), 289-324. | MR 58 #28261a | Zbl 0369.22009
[10] , , , Orbit structure and countable sections for actions of continuous groups, Adv. in Math., 28 (1978), 186-230. | MR 58 #11217 | Zbl 0392.28023
[11] , A Poisson formula for semisimple Lie groups, Annals of Math., 77 (1963), 335-383. | MR 26 #3820 | Zbl 0192.12704
[12] , Ergodic Theory, New York, Chelsea, 1956. | MR 20 #3958 | Zbl 0073.09302
[13] , , Geometry of horospheres, J. Diff. Geom., 12 (1977), 481-491. | MR 80a:53051 | Zbl 0434.53038
[14] , , Foliated bundles, invariant measures, and flat manifolds, Annals of Math., 101 (1975), 369-390. | MR 51 #6842 | Zbl 0321.57015
[15] , Certain quotient spaces are countably separated, III, J. Funct. Anal., 22 (1976), 225-241. | MR 54 #5385 | Zbl 0334.22005
[16] , Borel structures in groups and their duals, Trans. Amer. Math. Soc., 85 (1957), 134-165. | MR 19,752b | Zbl 0082.11201
[17] , Point realizations of transformation groups, Ill. J. Math., 6 (1962), 327-335. | MR 26 #1424 | Zbl 0178.17203
[18] , Ergodic theory and virtual groups, Math. Ann., 166 (1966), 187-207. | MR 34 #1444 | Zbl 0178.38802
[19] , Discrete groups of motions of manifolds of non-positive curvature, Amer. Math. Soc. Translations, 109 (1977), 33-45. | Zbl 0367.57012
[20] , Factor groups of discrete subgroups, Soviet Math. Dokl., 19 (1978), 1145-1149. | Zbl 0429.20044
[21] , Quotient groups of discrete subgroups and measure theory, Funct. Anal. Appl., 12 (1978), 295-305. | MR 80k:22005 | Zbl 0423.28012
[22] , Compactifications of symmetric spaces, Amer. J. Math., 86 (1964), 201-218. | MR 28 #5146 | Zbl 0156.03202
[23] , Ergodicity of flows on homogeneous spaces, Amer. J. Math., 88 (1966), 154-178. | MR 33 #1409 | Zbl 0148.37902
[24] , 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 38 #4679 | Zbl 0189.09402
[25] , Strong rigidity of locally symmetric spaces, Annals of Math. Studies, No. 78, Princeton University Press, 1973. | MR 52 #5874 | Zbl 0265.53039
[26] , , Ergodic Theory of amenable group actions, I, Bull. Amer. Math. Soc., 2 (1980), 161. | MR 80j:28031 | Zbl 0427.28018
[27] , Virtual groups and group actions, Adv. in Math., 6 (1971), 253-322. | MR 43 #7590 | Zbl 0216.14902
[28] , , Currents, flows, and diffeomorphisms, Topology, 14 (1975), 319-327. | MR 54 #3759 | Zbl 0321.58019
[29] , On representations and compactifications of symmetric Riemannian spaces, Annals of Math., 71 (1960), 77-110. | MR 22 #9546 | Zbl 0094.34603
[30] , Foliations of polynomial growth are hyperfinite, Israel J. Math., 34 (1979), 245-258. | MR 82i:28019 | Zbl 0436.28015
[31] , Amenable ergodic group actions and an application to Poisson boundaries of random walks, J. Funct. Anal., 27 (1978), 350-372. | MR 57 #12775 | Zbl 0391.28011
[32] , Hyperfinite factors and amenable ergodic actions, Invent. Math., 41 (1977), 23-31. | MR 57 #10438 | Zbl 0361.46061
[33] , Induced and amenable ergodic actions of Lie groups, Ann. Sci. Ec. Norm. Sup., 11 (1978), 407-428. | Numdam | MR 81b:22013 | Zbl 0401.22009
[34] , Orbit spaces of unitary representations, ergodic theory, and simple Lie groups, Annals of Math., 106 (1977), 573-588. | MR 57 #6286 | Zbl 0393.22006
[35] , Algebraic topology of ergodic Lie group actions and measurable foliations, preprint.
[36] , Strong rigidity for ergodic actions of semisimple Lie groups, Annals of Math., 112 (1980), 511-529. | MR 82i:22011 | Zbl 0468.22011
[37] , Orbit equivalence and rigidity of ergodic actions of Lie groups, Ergodic Theory and Dynamical Systems, 1 (1981), 237-253. | MR 84a:22019 | Zbl 0485.22013
[38] , On the Mostow rigidity theorem and measurable foliations by hyperbolic space, Israel J. Math., to appear. | Zbl 0554.58035
[39] , Curvature of leaves of amenable foliations, American J. Math., to appear. | Zbl 0527.57015
[40] , , Some smooth ergodic systems, Russian Math. Surveys, 22 (1967), 103-67. | Zbl 0177.42002
[41] , Lattices in spaces of nonpositive curvature, Annals of Math., 111 (1980), 435-467. | MR 82m:53040 | Zbl 0401.53015