Skip to main content
Log in

Spectrum, entropy, and geometric structures for smooth actions of kazhdan groups

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We show that many natural classes of actions of discrete subgroups of semisimple Lie groups have discrete spectrum, i.e., are measurably conjugate to isometric actions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. G. W. Mackey,Ergodic transformation groups with a pure point spectrum, Ill. J. Math.6 (1962), 327–335.

    MATH  MathSciNet  Google Scholar 

  2. G. A. Margulis,Discrete Subgroups of Semisimple Lie Groups, Springer, Berlin (to appear).

  3. J. Moser,On the volume elements on a manifold, Trans. Amer. Math. Soc.120 (1965), 286–294.

    Article  MATH  MathSciNet  Google Scholar 

  4. R. J. Zimmer,Ergodic actions with generalized discrete spectrum, Ill. J. Math.20 (1976), 555–588.

    MATH  MathSciNet  Google Scholar 

  5. R. J. Zimmer,Volume preserving actions of lattices in semisimple groups on compact manifolds, Publ. Math. I.H.E.S.59 (1984), 5–33.

    MATH  MathSciNet  Google Scholar 

  6. R. J. Zimmer,Kazhdan groups acting on compact manifolds, Invent. Math.75 (1984), 425–436.

    Article  MATH  MathSciNet  Google Scholar 

  7. R. J. Zimmer,Lattices in semismple groups and invariant geometric structures on compact manifolds, inDiscrete Groups in Geometry and Analysis (R. Howe, ed.), Birkhauser, Boston, 1987, pp. 152–210.

    Google Scholar 

  8. R. J. Zimmer,Ergodic Theory and Semisimple Groups, Birkhauser, Boston, 1984.

    MATH  Google Scholar 

  9. R. J. Zimmer,Actions of semisimple groups and discrete groups, Proc. ICM, Berkeley, 1986, pp.1247–1258.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research partially supported by NSF Grant.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zimmer, R.J. Spectrum, entropy, and geometric structures for smooth actions of kazhdan groups. Israel J. Math. 75, 65–80 (1991). https://doi.org/10.1007/BF02787182

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02787182

Keywords

Navigation