Inventiones mathematicae

, Volume 19, Issue 4, pp 279–330

On the heat equation and the index theorem

  • M. Atiyah
  • R. Bott
  • V. K. Patodi
Article
  • 1.4k Downloads

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Atiyah, M.F., Singer, I.M.: The index of elliptic operators, I. Ann. of Math.87, 484–530 (1968).Google Scholar
  2. 2.
    Atiyah, M.F., Singer, I.M.; The index of elliptic operators, III. Ann. of Math.87, 546–604 (1968).Google Scholar
  3. 3.
    Atiyah, M.F., Singer, I.M.: The index of elliptic operators, IV. Ann. of Math.93, 119–138 (1971).Google Scholar
  4. 4.
    Atiyah, M.F., Singer, I.M.: The index of elliptic operators, V. Ann. of Math.93, 139–149 (1971).Google Scholar
  5. 5.
    Atiyah, M.F., Singer, I.M.: The index of elliptic operators on compact manifolds. Bull. Amer. Math. Soc.69, 422–433 (1963).Google Scholar
  6. 6.
    Atiyah, M.F., Bott, R.: A Lefschetz fixed point formula for elliptic complexes, I. Ann. of Math.86, 374–407 (1967).Google Scholar
  7. 7.
    Atiyah, M.F., Bott, R.: A Lefschetz fixed point formula for elliptic complexes, II. Ann. of Math.88, 451–491 (1968).Google Scholar
  8. 8.
    Atiyah, M.F., Bott, R., Shapiro, A.: Clifford modules. Topology3, Suppl. 1, 3–38 (1964).CrossRefGoogle Scholar
  9. 9.
    Atiyah, M.F., Hirzebruch, F.: Spin-manifolds and group actions. Essays on Topology and related topics dedicated to G. de Rham. Berlin-Heidelberg-New York: Springer 1970.Google Scholar
  10. 10.
    Berger, M.: Le spectre d'une variété riemannienne. Lecture Notes in Mathematics194. Berlin-Heidelberg-New York: Springer 1971.Google Scholar
  11. 11.
    Bott, R.: Vector fields and characteristic numbers. Mich. Math. J.14, 231–244 (1967).CrossRefGoogle Scholar
  12. 12.
    Bott, R.: The periodicity theorem for the classical groups and some of its applications. Advances in Math.4, 353–411 (1970).CrossRefGoogle Scholar
  13. 13.
    Eisenhart, L.: Introduction to Differential Geometry. Princeton: University Press 1940.Google Scholar
  14. 14.
    Gel'fand, I.M.: The cohomology of some infinite-dimensional Lie algebras. Proceedings of International Congress, Nice,I, 95–110 (1970).Google Scholar
  15. 15.
    Gilkey, P.: Curvature and the eigenvalues of the Laplacian for elliptic complexes. Advances in Mathematics (to appear).Google Scholar
  16. 16.
    Hirzebruch, F.: Topological methods in algebraic geometry. Berlin-Heidelberg-New York: Springer 1966.Google Scholar
  17. 17.
    Hitchin, N.: Harmonic Spinors (to appear).Google Scholar
  18. 18.
    McKean, H. P., Jr., Singer, I. M.: Curvature and the eigenvalues of the Laplacian. J. Differential Geometry1, 43–69 (1967).Google Scholar
  19. 19.
    Minakshisundaram, S., Pleijel, A.: Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds. Canadian J. Math.1, 242–256 (1949).Google Scholar
  20. 20.
    Palais, R.: Seminar on the Atiyah-Singer Index Theorem. Ann. of Math. Studies57, Princeton, 1965.Google Scholar
  21. 21.
    Patodi, V.K.: Curvature and the eigenforms of the Laplace operator. J. Diff. Geometry5, 233–249 (1971).Google Scholar
  22. 22.
    Patodi, V.K.: An analytic proof of Riemann-Roch-Hirzebruch theorem for Kaehler manifolds. J. Diff. Geometry5, 251–283 (1971).Google Scholar
  23. 23.
    Seeley, R.T.: Complex powers of an elliptic operator. Proc. Sympos. Pure Math.10, Amer. Math. Soc. 288–307, 1967.Google Scholar
  24. 24.
    Weyl, H.: The classical groups, Princeton University Press, Princeton, 1946.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • M. Atiyah
    • 1
  • R. Bott
    • 2
  • V. K. Patodi
    • 3
    • 4
  1. 1.Mathematical InstituteOxfordEngland
  2. 2.Department of MathematicsHarvard UniversityCambridgeUSA
  3. 3.Institute for Advanced StudyPrincetonUSA
  4. 4.School of MathematicsTata Institute of Fundamental ResearchBombay 5India

Personalised recommendations