Deformation rigidity for subgroups of 𝑆𝐿(𝑛,𝐙) acting on the 𝐧-torus

Hurder, Steven

doi:10.1090/S0273-0979-1990-15914-2

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

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