First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity

Anatole Katok; Ralph J. Spatzier

Publications Mathématiques de l'IHÉS (1994)

  • Volume: 79, page 131-156
  • ISSN: 0073-8301

How to cite

top

Katok, Anatole, and Spatzier, Ralph J.. "First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity." Publications Mathématiques de l'IHÉS 79 (1994): 131-156. <http://eudml.org/doc/104094>.

@article{Katok1994,
author = {Katok, Anatole, Spatzier, Ralph J.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {-action; -action; Anosov actions; rigidity},
language = {eng},
pages = {131-156},
publisher = {Institut des Hautes Études Scientifiques},
title = {First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity},
url = {http://eudml.org/doc/104094},
volume = {79},
year = {1994},
}

TY - JOUR
AU - Katok, Anatole
AU - Spatzier, Ralph J.
TI - First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity
JO - Publications Mathématiques de l'IHÉS
PY - 1994
PB - Institut des Hautes Études Scientifiques
VL - 79
SP - 131
EP - 156
LA - eng
KW - -action; -action; Anosov actions; rigidity
UR - http://eudml.org/doc/104094
ER -

References

top
  1. [1] W. CASSELMAN and D. MILIČIČ, Asymptotic behavior of matrix coefficients of admissible representations, Duke J. of Math., 49 (1982), 869-930. Zbl0524.22014MR85a:22024
  2. [2] M. COWLING, Sur les coefficients des représentations unitaires des groupes de Lie simple, Lecture Notes in Mathematics, 739, 1979, 132-178, Springer Verlag. Zbl0417.22010MR81e:22019
  3. [3] Harish CHANDRA, Spherical functions on a semisimple Lie group, I, Amer J. of Math., 80 (1958), 241-310. Zbl0093.12801MR20 #925
  4. [4] M. HIRSCH, C. PUGH and M. SHUB, Invariant manifolds, Lecture Notes in Mathematics, 583, Springer Verlag, Berlin, 1977. Zbl0355.58009MR58 #18595
  5. [5] R. HOWE, A notion of rank for unitary representations of the classical groups, in A. FIGÀ TALAMANGA (ed.), Harmonic analysis and group representations, CIME, 1980. 
  6. [6] S. HURDER and A. KATOK, Differentiability, rigidity and Godbillon-Vey classes for Anosov flows, Publ. Math. IHES, 72 (1990), 5-61. Zbl0725.58034MR92b:58179
  7. [7] H.-C. IMHOF, An Anosov action on the bundle of Weyl chambers, Ergod. Th. and Dyn. Syst., 5 (1985), 587-599. Zbl0555.58023MR87g:58103
  8. [8] J.-L. JOURNÉ, On a regularity problem occurring in connection with Anosov diffeomorphisms, Comm. Math. Phys., 106 (1986), 345-352. Zbl0603.58019MR88b:58103
  9. [9] J.-L. JOURNÉ, A regularity lemma for functions of several variables, Revista Math. Iber., 4 (2), (1988), 187-193. Zbl0699.58008MR91j:58123
  10. [10] A. KATOK and R. J. SPATZIER, Cocycle rigidity of partially hyperbolic actions of higher rank abelian groups, Math. Res. Letters, 1 (1994), 193-202. Zbl0836.57026MR95b:35042
  11. [11] A. KATOK and R. J. SPATZIER, Differential rigidity of Anosov actions of higher rank Abelian groups, in preparation. Zbl0938.37010
  12. [12] A. KATOK and R. J. SPATZIER, Differential rigidity of projective lattice actions, in preparation. Zbl0938.37010
  13. [13] A. KATOK and R. J. SPATZIER, Invariant measures for higher rank hyperbolic abelian actions, MSRI preprint, 059-92, Berkeley, 1992. 
  14. [14] A. LIVSHITZ, Cohomology of dynamical systems, Math. U.S.S.R. Izvestija, 6 (1972), 1278-1301. Zbl0273.58013
  15. [15] R. de LA LLAVÉ, J. 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. Zbl0603.58016MR88h:58091
  16. [16] G. A. MARGULIS, Discrete subgroups of semisimple Lie groups, Springer Verlag, Berlin, 1991. Zbl0732.22008MR92h:22021
  17. [17] C. C. MOORE, Exponential decay of correlation coefficients for geodesic flows, in C. C. MOORE (ed), Group representations, ergodic theory, operator algebras, and mathematical physics, Proceedings of a Conference in Honor of George Mackey, MSRI publications, Springer Verlag, 1987, 163-181. Zbl0625.58023MR89d:58102
  18. [18] C. PUGH and M. SHUB, Ergodicity of Anosov actions, Inventiones Math., 15 (1972), 1-23. Zbl0236.58007MR45 #4456
  19. [19] N. QIAN, Rigidity Phenomena of Group Actions on a Class of Nilmanifolds and Anosov Rn-Actions, Ph.D. thesis, California Institute of Technology, 1992. 
  20. [20] M. RAGHUNATHAN, Discrete subgroups of Lie groups, Springer Verlag, New York, 1972. Zbl0254.22005MR58 #22394a
  21. [21] M. RATNER, The rate of mixing for geodesic and horocycle flows, Ergod. Th. and Dyn. Syst., 7 (1987), 267-288. Zbl0623.22008MR88j:58103
  22. [22] G. WARNER, Harmonic Analysis on semisimple Lie groups I, Springer Verlag, Berlin, 1972. Zbl0265.22020
  23. [23] R. J. ZIMMER, Ergodic theory and semisimple groups, Boston, Birkhäuser, 1984. Zbl0571.58015MR86j:22014

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.