previous :: next
On Livšic’s theorem, superrigidity, and Anosov actions of semisimple Lie groups
Edward R. Goetze and Ralf J. Spatzier
Source: Duke Math. J. Volume 88, Number 1
(1997), 1-27.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077241397
Mathematical Reviews number (MathSciNet): MR1448015
Zentralblatt MATH identifier: 0879.22004
Digital Object Identifier: doi:10.1215/S0012-7094-97-08801-3
References
[1] D. V. Anosov, Geodesic flows on closed Riemann manifolds with negative curvature. , Proceedings of the Steklov Institute of Mathematics, No. 90 (1967). Translated from the Russian by S. Feder, American Mathematical Society, Providence, R.I., 1969.
Mathematical Reviews (MathSciNet): MR39:3527
Zentralblatt MATH: 0176.19101
[2] A. Borel and N. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Annals of Mathematics Studies, vol. 94, Princeton University Press, Princeton, N.J., 1980.
Mathematical Reviews (MathSciNet): MR83c:22018
Zentralblatt MATH: 0443.22010
[3] R. Feres, Connection preserving actions of lattices in $\rm SL\sb n\bf R$, Israel J. Math. 79 (1992), no. 1, 1–21.
Mathematical Reviews (MathSciNet): MR94a:58039
Zentralblatt MATH: 0786.57016
Digital Object Identifier: doi:10.1007/BF02764799
[4] H. Furstenberg, Rigidity and cocycles for ergodic actions of semisimple Lie groups (after G. A. Margulis and R. Zimmer), Bourbaki Seminar, Vol. 1979/80, Lecture Notes in Math., vol. 842, Springer, Berlin, 1981, pp. 273–292.
Mathematical Reviews (MathSciNet): MR83j:22003
Zentralblatt MATH: 0471.22007
Digital Object Identifier: doi:10.1007/BFb0089940
[5] E. R. Goetze, Actions of superrigid non-Kazhdan lattices on compact manifolds, Geom. Dedicata 53 (1994), no. 3, 281–285.
Mathematical Reviews (MathSciNet): MR96c:22018
Zentralblatt MATH: 0833.22016
Digital Object Identifier: doi:10.1007/BF01264001
[6] E. R. Goetze, Connection preserving actions of connected and discrete Lie groups, J. Differential Geom. 40 (1994), no. 3, 595–620.
Mathematical Reviews (MathSciNet): MR95m:57052
Zentralblatt MATH: 0846.57030
Project Euclid: euclid.jdg/1214455779
[7] E. R. Goetze and R. J. Spatzier, Bundle theoretic versions of Livšic's theory, in preparation.
[8] E. R. Goetze and R. J. Spatzier, Smooth classification of Cartan actions of higher rank semisimple Lie groups and their lattices, preprint.
Mathematical Reviews (MathSciNet): MR1740993
Zentralblatt MATH: 0940.22011
Digital Object Identifier: doi:10.2307/121055
JSTOR: links.jstor.org
[9] M. W. Hirsch, C. C. Pugh, and M. Shub, Invariant Manifolds, Lecture Notes in Math., vol. 583, Springer-Verlag, Berlin, 1977.
Mathematical Reviews (MathSciNet): MR58:18595
Zentralblatt MATH: 0355.58009
[10] J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics, vol. 9, Springer-Verlag, New York, 1978.
Mathematical Reviews (MathSciNet): MR81b:17007
Zentralblatt MATH: 0447.17001
[11] S. Hurder, Rigidity for Anosov actions of higher rank lattices, Ann. of Math. (2) 135 (1992), no. 2, 361–410.
Mathematical Reviews (MathSciNet): MR93c:22018
Zentralblatt MATH: 0754.58029
Digital Object Identifier: doi:10.2307/2946593
[12] A. B. Katok and J. W. Lewis, Global rigidity results for lattice actions on tori and new examples of volume-preserving actions, Israel J. Math. 93 (1996), 253–280.
Mathematical Reviews (MathSciNet): MR96k:22021
Zentralblatt MATH: 0857.57038
Digital Object Identifier: doi:10.1007/BF02761106
[13] A. B. Katok and J. W. Lewis, Local rigidity for certain groups of toral automorphisms, Israel J. Math. 75 (1991), no. 2-3, 203–241.
Mathematical Reviews (MathSciNet): MR93g:58076
Zentralblatt MATH: 0785.22012
Digital Object Identifier: doi:10.1007/BF02776025
[14] A. B. Katok, J. W. Lewis, and R. J. Zimmer, Cocycle superrigidity and rigidity for lattice actions on tori, Topology 35 (1996), no. 1, 27–38.
Mathematical Reviews (MathSciNet): MR97e:22009
Zentralblatt MATH: 0857.57037
Digital Object Identifier: doi:10.1016/0040-9383(95)00012-7
[15] J. W. Lewis, Infinitesimal rigidity for the action of $\rm SL(n,\bf Z)$ on $\bf T\sp n$, Trans. Amer. Math. Soc. 324 (1991), no. 1, 421–445.
Mathematical Reviews (MathSciNet): MR91f:22019
Zentralblatt MATH: 0726.57028
Digital Object Identifier: doi:10.2307/2001516
[16] A. N. Livšic, Cohomology of dynamical systems, Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972), 1296–1320.
Mathematical Reviews (MathSciNet): MR48:12606
[17] R. Mañé, Ergodic theory and differentiable dynamics, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 8, Springer-Verlag, Berlin, 1987.
Mathematical Reviews (MathSciNet): MR88c:58040
Zentralblatt MATH: 0616.28007
[18] C. Pugh and M. Shub, Ergodicity of Anosov actions, Invent. Math. 15 (1972), 1–23.
Mathematical Reviews (MathSciNet): MR45:4456
Zentralblatt MATH: 0236.58007
Digital Object Identifier: doi:10.1007/BF01418639
[19] N. Qian, Smooth conjugacy for Anosov diffeomorphisms and rigidity of Anosov actions of higher rank lattices, preprint.
[20] N. Qian, Tangential flatness and global rigidity of higher rank lattice actions, to appear in Trans. Amer. Math. Soc.
Mathematical Reviews (MathSciNet): MR1401783
Zentralblatt MATH: 0877.22003
Digital Object Identifier: doi:10.1090/S0002-9947-97-01857-6
JSTOR: links.jstor.org
[21] N. Qian, Topological deformation rigidity of higher rank lattice actions, Math. Res. Lett. 1 (1994), no. 4, 485–499.
Mathematical Reviews (MathSciNet): MR95i:58144
Zentralblatt MATH: 0836.22016
[22] W. Rudin, Real and Complex Analysis, 3rd ed. ed., McGraw-Hill Book Co., New York, 1987.
Mathematical Reviews (MathSciNet): MR88k:00002
Zentralblatt MATH: 0925.00005
[23] R. J. Zimmer, Ergodic Theory and Semisimple Groups, Monographs in Mathematics, vol. 81, Birkhäuser, Basel, 1984.
Mathematical Reviews (MathSciNet): MR86j:22014
Zentralblatt MATH: 0571.58015
[24] R. J. Zimmer, On the algebraic hull of an automorphism group of a principal bundle, Comment. Math. Helv. 65 (1990), no. 3, 375–387.
Mathematical Reviews (MathSciNet): MR92f:57050
Zentralblatt MATH: 0733.54028
Digital Object Identifier: doi:10.1007/BF02566614
[25] R. J. Zimmer, Topological superrigidity, preprint.
previous :: next
Duke Mathematical Journal
