Advertisement

Spin-Manifolds and Group Actions

  • Michael Atiyah
  • Friedrich Hirzebruch

Abstract

Let X be a compact oriented differentiable n-dimensional manifold (all manifolds are without boundary except in § 4) on which a Riemannian metric is introduced. Let Q be the principal tangential SO (n)-bundle of X.

Keywords

Complex Vector Bundle Positive Imaginary Part Lefschetz Theorem Pontrjagin Class Quaternionic Projective Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [1]
    Atiyah, M. F., and R. Bott: A Lefschetz fixed point formula for elliptic complexes, II. Applications. Ann. of Math. 88, 451–491 (1968).MathSciNetzbMATHGoogle Scholar
  2. [2]
    Atiyah, M. F., and I. M. Singer: The index of elliptic operators, III. Ann. of Math. 87, 546–604 (1968).MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    Borel, A., and F. Hirzebruch: Characteristic classes and homogeneous spaces, I. Amer. J. of Math. 80, 458–538 (1958).MathSciNetCrossRefGoogle Scholar
  4. [4.
    Characteristic classes and homogeneous spaces, II. Amer. J. of Math. 81, 315–382 (1959).Google Scholar
  5. [5]
    Hirzebruch, F.: Topological methods in algebraic geometry. Third enlarged edition, Berlin-Heidelberg-New York: Springer 1966.Google Scholar
  6. [6]
    Kosniowski, C.: Applications of the holomorphic Lefschetz formula. Bull. London Math. Soc. 1969. [To appear.]Google Scholar
  7. [7]
    Lichnerowicz, A.: Spineurs harmoniques. Paris: C. R. Acad. Sci. 257, 7–9 (1963).MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1970

Authors and Affiliations

  • Michael Atiyah
  • Friedrich Hirzebruch

There are no affiliations available

Personalised recommendations