Skip to main content
SpringerLink
Log in

Thee-invariant and the spectrum of the Laplacian for compact nilmanifolds covered by Heisenberg groups

  • Published:
Inventiones mathematicae Aims and scope

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Adams, J.F.: On the groupsJ (X)-IV. Topology5, 21–71 (1966)

    Google Scholar 

  2. Atiyah, M.F., Bott, R.: A Lefschetz fixed point formula for elliptic complexes—II. Applications. Ann. Math.88, 451–491 (1968)

    Google Scholar 

  3. Atiyah, M.F., Bott, R., Shapiro, A.: Clifford modules. Topology3, (Suppl. 1) 3–38 (1964)

    Google Scholar 

  4. Atiyah, M.F., Patodi, V.K., Singer, I.M.: Spectral asymmetry and Riemannian geometry. II. Math. Proc. Camb. Phil. Soc.78, 405–432 (1975)

    Google Scholar 

  5. Atiyah, M.F., Patodi, V.K., Singer, I.M.: Spectral asymmetry and Riemannian geometry. III. Math. Proc. Camb. Phil Soc.79, 71–99 (1976)

    Google Scholar 

  6. Atiyah, M.F., Smith, L.: Compact Lie groups and the stable homotopy of spheres. Topology13, 135–142 (1974)

    Google Scholar 

  7. Howe, R.: On Frobenius reciprocity for unipotent algebraic groups overQ Amer. J. of Math.93, 163–172 (1971)

    Google Scholar 

  8. Kamke, E.: Differentialgleichungen. Lösungsmethoden und Lösungen, Bd. I, 5. Auflage. Leipzig: Akademische Verlagsgesellschaft 1956

    Google Scholar 

  9. Kirillov, A.A.: Unitary representations of niloptent Lie groups. Russian Math. Surveys17, (No. 4) 53–104 (1962)

    Google Scholar 

  10. Milnor, J.: On the 3-dimensional Brieskorn manifoldM (p,q,r), In: Knots, Groups and 3-Manifolds, p. 175–225. Neuwirth, L. P. (ed.). Ann. of Math. Study No. 84. Princeton: Princeton University Press 1975

    Google Scholar 

  11. Neumann, J. v.: Die Eindeutigkeit der Schrödingerschen Operatoren. Math. Ann.104, 570–578 (1931)

    Google Scholar 

  12. Richardson, L.F.: Decomposition of theL 2-space of a general compact nilmanifold. Amer. J. of Math.93, 173–190 (1971)

    Google Scholar 

  13. Seade, J.A.: Singular points of complex surfaces and homotopy. Topology21, 1–8 (1982)

    Google Scholar 

  14. Seade, J.A., Steer, B.: The elements of π S3 represented by invariant framings of quotients of\(\widetilde{SL}_2 \) (ℝ) by certain discrete subgroups. Adv. in Math.46, 221–229 (1982)

    Google Scholar 

  15. Singhof, W.: Thed-invariant of compact nilmanifolds. Invent. Math.78, 113–115 (1984)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Universität Regensburg, Universitätsstr. 31, D-8400, Regensburg 2, Federal Republic of Germany

    Ch. Deninger

  2. Mathematisches Institut, Universität Köln, Weyertal 86-90, D-5000, Köln 41, Federal Republic of Germany

    W. Singhof

Authors
  1. Ch. Deninger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Singhof
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deninger, C., Singhof, W. Thee-invariant and the spectrum of the Laplacian for compact nilmanifolds covered by Heisenberg groups. Invent Math 78, 101–112 (1984). https://doi.org/10.1007/BF01388716

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388716

Keywords

Search

Navigation