Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Deformation rigidity for subgroups of $SL\left( {n,{\mathbf{Z}}} \right)$ acting on the $n$-torus


Author: Steven Hurder
Journal: Bull. Amer. Math. Soc. 23 (1990), 107-113
MSC (1985): Primary 57S25, 58H15, 22E40
DOI: https://doi.org/10.1090/S0273-0979-1990-15914-2
MathSciNet review: 1027900
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. D. V. Anosov, Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Inst. Math. 90 (1967), Amer. Math. Soc. Transl. (1969), 5-209. MR 224110
  • 2. A. Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. (4) 7 (1974), 235-272. MR 387496
  • 3. A. Borel, Stable real cohomology of arithmetic groups II, in Manifolds and Lie Groups, Papers in Honor of Yozo Matsushima, Prog. Math. 14 (1981), 21-55. MR 642850
  • 4. L. Flamino and A. Katok, Rigidity of symplectic Anosov diffeomorphisms on low dimensional tori, Cal. Tech., preprint, 1989.
  • 5. J. Franks, Anosov diffeomorphisms on tori, Trans. Amer. Math. Soc. 145 (1969), 117-124. MR 253352
  • 6. M. W. Hirsch, C. Pugh and M. Snub, Invariant manifolds, Lecture Notes in Math., Vol. 583, Springer-Verlag, Berlin, 1977. MR 501173
  • 7. S. Hurder, Deformation rigidity and structural stability for Anosov actions of higher-rank lattices, preprint.
  • 8. S. Hurder, Problems on rigidity of group actions and cocycles, Ergodic Theory Dynamical Systems 5 (1985), 473-484. MR 805843
  • 9. S. Hurder and A. Katok, Differentiability, rigidity and Godbillon-Vey classes for Anosov flows, Publications Inst. Hautes Etudes Sci. (revision to appear). MR 1087392
  • 10. J. Lewis, Infinitesimal rigidity for the action of SL(n, Z) on T, Thesis, University of Chicago, May, 1989.
  • 11. A. Livsic, Cohomology of dynamical systems, Math. USSR Izv. 6 (1972), 1278-1301. MR 334287
  • 12. R. de la Llavé, Invariants for smooth conjugacy of hyperbolic dynamical systems II, Commun. Math. Phys. 109 (1987), 369-378. MR 882805
  • 13. R. de la Llavé, J. M. Marco and R. Moriyon, Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation, Ann. of Math. 123 (1986), 537-611. MR 840722
  • 14. J. M. Marco and R. Moriyon, Invariants for smooth conjugacy of hyperbolic dynamical systems I, Commun. Math. Phys. 109 (1987), 681-689. MR 885566
  • 15. G. A. Margulis, Discrete subgroups of Lie groups, Springer-Verlag (to appear). MR 1090825
  • 16. G. Prasad and M. S. Raghunathan, Cartan subgroups and lattices in semisimple groups, Ann. of Math. 96 (1972), 296-317. MR 302822
  • 17. M. Shub, Global stability of dynamical systems, Springer-Verlag, Berlin, 1987. MR 869255
  • 18. D. Stowe, The stationary set of a group action, Proc. Amer. Math. Soc. 79 (1980), 139-146. MR 560600
  • 19. R. Zimmer, Lattices in semi-simple groups and invariant geometric structures on compact manifolds, in Discrete Groups in Geometry and Analysis: Papers in Honor of G. D. Mostow on his sixtieth birthday (Roger Howe, ed.), Prog. Math. 67 (1987), 152-210. MR 900826

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 57S25, 58H15, 22E40

Retrieve articles in all journals with MSC (1985): 57S25, 58H15, 22E40


Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1990-15914-2

American Mathematical Society