Volume preserving actions of lattices in semisimple groups on compact manifolds

Robert Zimmer

Publications Mathématiques de l'IHÉS (1984)

  • Volume: 59, page 5-33
  • ISSN: 0073-8301

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Zimmer, Robert. "Volume preserving actions of lattices in semisimple groups on compact manifolds." Publications Mathématiques de l'IHÉS 59 (1984): 5-33. <http://eudml.org/doc/104000>.

@article{Zimmer1984,
author = {Zimmer, Robert},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {volume preserving actions; lattices; semisimple Lie groups; compact manifolds; superrigidity theorem for cocycles; Riemannian metric},
language = {eng},
pages = {5-33},
publisher = {Institut des Hautes Études Scientifiques},
title = {Volume preserving actions of lattices in semisimple groups on compact manifolds},
url = {http://eudml.org/doc/104000},
volume = {59},
year = {1984},
}

TY - JOUR
AU - Zimmer, Robert
TI - Volume preserving actions of lattices in semisimple groups on compact manifolds
JO - Publications Mathématiques de l'IHÉS
PY - 1984
PB - Institut des Hautes Études Scientifiques
VL - 59
SP - 5
EP - 33
LA - eng
KW - volume preserving actions; lattices; semisimple Lie groups; compact manifolds; superrigidity theorem for cocycles; Riemannian metric
UR - http://eudml.org/doc/104000
ER -

References

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  1. [1] C. DELAROCHE and A. KIRILLOV, Sur les relations entre l'espace dual d'un groupe et la structure de ses sous-groupes fermés, Séminaire Bourbaki, No. 343 (1967/1968). Zbl0214.04602
  2. [2] Y. DERRIENNIC, Sur le théorème ergodique sous-additif, C. R. Acad. Sci. 281, Paris (1975), Série A, 985-988. Zbl0327.60028MR53 #763
  3. [3] H. FURSTENBERG and H. KESTEN, Products of random matrices, Ann. Math. Stat. 31 (1960), 457-469. Zbl0137.35501MR22 #12558
  4. [4] H. FURSTENBERG, Rigidity and cocycles for ergodic actions of semisimple groups [after G. A. Margulis and R. Zimmer], Séminaire Bourbaki, No. 559 (1979/1980). Zbl0471.22007
  5. [5] S. HELGASON, Differential Geometry and Symmetric Spaces, New York, Academic Press, 1962. Zbl0111.18101MR26 #2986
  6. [6] D. KAZHDAN, Connection of the dual space of a group with the structure of its closed subgroups, Funct. Anal. Appl. 1 (1967), 63-65. Zbl0168.27602MR35 #288
  7. [7] J. F. C. KINGMAN, The ergodic theory of subadditive stochastic processes, J. Royal Stat. Soc. B30 (1968), 499-510. Zbl0182.22802MR40 #8114
  8. [8] S. KOBAYASHI, Transformation groups in differential geometry, New York, Springer, 1972. Zbl0246.53031MR50 #8360
  9. [9] G. A. MARGULIS, Discrete groups of motions of manifolds of non-positive curvature, A.M.S. Translations 109 (1977), 33-45. Zbl0367.57012
  10. [10] D. MONTGOMERY and L. ZIPPIN, Topological Transformation Groups, New York, Interscience, 1955. Zbl0068.01904MR17,383b
  11. [11] G. D. MOSTOW, Strong rigidity of locally symmetric spaces, Annals of Math. Studies, No. 78 (1973). Zbl0265.53039MR52 #5874
  12. [12] G. D. MOSTOW, Intersection of discrete subgroups with Cartan subgroups, J. Indian Math. Soc. 34 (1970), 203-214. Zbl0235.22019MR58 #11228
  13. [13] R. PALAIS, Seminar on the Atiyah-Singer Index Theorem, Annals of Math. Studies, No. 57. Zbl0202.23103MR33 #6649
  14. [14] Ya. B. PESIN, Lyapunov characteristic exponents and smooth ergodic theory, Russian Math. Surveys 32 (1977), 55-114. Zbl0383.58011
  15. [15] G. PRASAD and M. S. RAGHUNATHAN, Cartan subgroups and lattices in semisimple groups, Annals of Math. 96 (1972), 296-317. Zbl0245.22013MR46 #1965
  16. [16] M. S. RAGHUNATHAN, On the congruence subgroup problem, Publ. Math. I.H.E.S. 46 (1976), 107-161. Zbl0347.20027MR58 #22325
  17. [17] K. SCHMIDT, Amenability, Kazhdan's property T, strong ergodicity, and invariant means for group actions, Erg. Th. and Dyn. Sys. 1 (1981), 223-236. Zbl0485.28019MR83m:43001
  18. [18] S. P. WANG, On isolated points in the dual spaces of locally compact groups, Math. Ann. 218 (1975), 19-34. Zbl0332.22009MR52 #5863
  19. [19] A. WEIL, On discrete subgroups of Lie groups, I, II, Annals of Math. 72 (1960), 369-384, and ibid., 75 (1962), 578-602. Zbl0131.26602
  20. [20] D. ZELOBENKO, Compact Lie groups and their representations, Translations of Math. Monographs, vol. 40, A.M.S., Providence, R.I., 1973. Zbl0272.22006MR57 #12776b
  21. [21] R. J. ZIMMER, Extensions of ergodic group actions, Ill. J. Math. 20 (1976), 373-409. Zbl0334.28015MR53 #13522
  22. [22] R. J. ZIMMER, Amenable pairs of ergodic actions and the associated von Neumann algebras, Trans. A.M.S. 243 (1978), 271-286. Zbl0408.22011MR81e:22008
  23. [23] R. J. ZIMMER, Orbit spaces of unitary representations, ergodic theory, and simple Lie groups, Annals of Math. 106 (1977), 573-588. Zbl0393.22006MR57 #6286
  24. [24] R. J. ZIMMER, An algebraic group associated to an ergodic diffeomorphism, Comp. Math. 43 (1981), 59-69. Zbl0491.58020MR83d:22006
  25. [25] R. J. ZIMMER, On the cohomology of ergodic actions of semisimple Lie groups and discrete subgroups, Amer. J. Math. 103 (1981), 937-950. Zbl0475.22011MR83g:28037
  26. [26] R. J. ZIMMER, Strong rigidity for ergodic actions of semisimple Lie groups, Annals of Math. 112 (1980), 511-529. Zbl0468.22011MR82i:22011
  27. [27] R. J. ZIMMER, Orbit equivalence and rigidity of ergodic actions of Lie groups, Erg. Th. and Dyn. Sys. 1 (1981), 237-253. Zbl0485.22013MR84a:22019
  28. [28] R. J. ZIMMER, Ergodic theory, group representations, and rigidity, Bull. A.M.S. 6 (1982), 383-416. Zbl0532.22009MR83k:22033
  29. [29] R. J. ZIMMER, Ergodic Theory and Semisimple Groups, forthcoming. Zbl0571.58015
  30. [30] R. J. ZIMMER, Arithmetic groups acting on compact manifolds, Bull. A.M.S., to appear. Zbl0532.22012

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