Global rigidity results for lattice actions on tori and new examples of volume-preserving actions

Israel Journal of Mathematics

Volumn 93, Issue , 1996, Pages 253-280

  Katok, A ^a   Lewis, J ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b Renaissance Software Inc   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030445427     PISSN: 00212172     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02761106     Document Type: Article

References (27)

1. 2n (n ≥ 2), Publications Mathématiques de l'Institue Hautes Études Scientifiques 33 (1967), 421-499.
2. A. Borel and J-P. Serre, Théorèmes de finitude en cohomologie galoisienne, Commentarii Mathematici Helvetici 39 (1964), 111-164.
3. 2 is rigid (i.e., topological conjugacy implies smooth conjugacy), a talk presented to the Lie groups and ergodic theory seminar at M.S.R.I., September, 1991.
4. J. Franks, Anosov diffeomorphisms, in Global Analysis, American Mathematical Society, Providence (Proceedings of Symposia in Pure Mathematics XIV), 1970.
5. E. Ghys, Actions localement libres du groupe affine, Inventiones Mathematicae 82 (1985), 479-526.
6. M. Gromov, Rigid transformation groups, in Géométrie différentielle, Travaux en cours 33, Herman, Paris, 1988.
7. S. Hurder, Problems on rigidity of group actions and cocycles, Ergodic Theory and Dynamical Systems 5 (1985), 473-484.
8. S. Hurder, Rigidity for Anosov actions of higher rank lattices, Annals of Mathematics 135 (1992), 361-410.
9. S. Hurder, Affine Anosov actions, The Michigan Mathematical Journal 40 (1993), 561-573.
10. A. Katok, Hyperbolicity and rigidity of actions of multi-parameter abelian groups, Workshop on Lie groups, ergodic theory and geometry, M.S.R.I., Berkeley, CA, 1992, pp. 36-40.
11. A. Katok and J. Lewis, Local rigidity for certain groups of toral automorphisms, Israel Journal of Mathematics 75 (1991), 203-241.
12. A. Katok, J. Lewis and R. Zimmer, Cocycle superrigidity and rigidity for lattice actions on tori, Topology (1995), to appear.
13. A. Katok and R. Spatzier, First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity, Publications Mathématiques de l'Institue Hautes Études Scientifiques 79 (1994), 131-156.
14. A. Katok and R. Spatzier, Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions, Mathematical Research Letters 1 (1994), 193-202.
15. A. N. Livshitz, Homology properties of Y-systems, Matematicheskie Zametki 10 (1971), 555-564, Russian; English translation: Mathematical Notes 10 (1971), 758-763.
16. A. N. Livshitz, Homology properties of Y-systems, Matematicheskie Zametki 10 (1971), 555-564, Russian; English translation: Mathematical Notes 10 (1971), 758-763.
17. R. de la Llave, J. M. Marco and R. Moriyon, Canonical perturbation theory of Anosov systems and regularity results for the Livshitz cohomology equation, Annals of Mathematics 123 (1986), 537-611.
18. A. Manning, There are no new Anosov diffeomorphisms on tori, American Journal of Mathematics 96 (1974), 422-429.
19. J. Palis and J.C. Yoccoz, Centralizers of Anosov diffeomorphisms on tori, Annales Scientifiques de l'École Normale Supérieure 22 (1989), 99-108.
20. M. Shub, Global Stability of Dynamical Systems, Springer-Verlag, New York, 1987.
21. Ya. Sinai, Gibbs measures in ergodic theory, Uspekhi Matematicheskikh Nauk 27 (1972), 21-64, Russian; English translation: Russian Mathematical Surveys 27 (1972), 21-69.
22. Ya. Sinai, Gibbs measures in ergodic theory, Uspekhi Matematicheskikh Nauk 27 (1972), 21-64, Russian; English translation: Russian Mathematical Surveys 27 (1972), 21-69.
23. D. Stowe, The stationary set of a group action, Proceedings of the American Mathematical Society 79 (1980), 139-146.
24. L. N. Vaserstein, Structure of classical arithmetic groups of rank greater than 1, Matematicheskii Sbornik 91 (1973), 465-492, Russian; English translation: Mathematics of the USSR-Sbornik 20 (1973), 445-470.
25. L. N. Vaserstein, Structure of classical arithmetic groups of rank greater than 1, Matematicheskii Sbornik 91 (1973), 465-492, Russian; English translation: Mathematics of the USSR-Sbornik 20 (1973), 445-470.
26. R. Zimmer, Actions of semisimple groups and discrete subgroups, Proceedings of the International Congress of Mathematicians (1986: Berkeley, CA), American Mathematical Society, Providence, RI, 1987, pp. 1247-1258.
27. R. Zimmer, Ergodic Theory and Semisimple Groups, Birkhäuser, Boston, 1984.