Bulletin (New Series) of the American Mathematical Society

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

Steven Hurder

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Bull. Amer. Math. Soc. (N.S.), Volume 23, Number 1 (1990), 107-113.

First available in Project Euclid: 4 July 2007

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Zentralblatt MATH identifier

Primary: 57S25: Groups acting on specific manifolds 58H15: Deformations of structures [See also 32Gxx, 58J10] 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]


Hurder, Steven. Deformation rigidity for subgroups of $SL\left( {n,{\mathbf{Z}}} \right)$ acting on the $n$-torus. Bull. Amer. Math. Soc. (N.S.) 23 (1990), no. 1, 107--113. https://projecteuclid.org/euclid.bams/1183555722

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  • 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.
  • 2. A. Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. (4) 7 (1974), 235-272.
  • 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.
  • 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.
  • 6. M. W. Hirsch, C. Pugh and M. Snub, Invariant manifolds, Lecture Notes in Math., Vol. 583, Springer-Verlag, Berlin, 1977.
  • 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.
  • 9. S. Hurder and A. Katok, Differentiability, rigidity and Godbillon-Vey classes for Anosov flows, Publications Inst. Hautes Etudes Sci. (revision to appear).
  • 10. J. Lewis, Infinitesimal rigidity for the action of SL(n, Z) on Tn, Thesis, University of Chicago, May, 1989.
  • 11. A. Livsic, Cohomology of dynamical systems, Math. USSR Izv. 6 (1972), 1278-1301.
  • 12. R. de la Llavé, Invariants for smooth conjugacy of hyperbolic dynamical systems II, Commun. Math. Phys. 109 (1987), 369-378.
  • 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.
  • 14. J. M. Marco and R. Moriyon, Invariants for smooth conjugacy of hyperbolic dynamical systems I, Commun. Math. Phys. 109 (1987), 681-689.
  • 15. G. A. Margulis, Discrete subgroups of Lie groups, Springer-Verlag (to appear).
  • 16. G. Prasad and M. S. Raghunathan, Cartan subgroups and lattices in semisimple groups, Ann. of Math. 96 (1972), 296-317.
  • 17. M. Shub, Global stability of dynamical systems, Springer-Verlag, Berlin, 1987.
  • 18. D. Stowe, The stationary set of a group action, Proc. Amer. Math. Soc. 79 (1980), 139-146.
  • 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.