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Inventiones mathematicae

, Volume 41, Issue 1, pp 1–22 | Cite as

The free loop space of globally symmetric spaces

  • Wolfgang Ziller
Article

Keywords

Symmetric Space Loop Space Free Loop 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.

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References

  1. 1.
    Araki, S.: On Bott-SamelsonK-cycles associated with a symmetric space. J. of Math. Osaka University13, 87–133 (1962)Google Scholar
  2. 2.
    Borel, A.: Sur la cohomologie des espaces fibres principaux et des espaces homogenes. Ann. of Math.57, 115–207 (1953)Google Scholar
  3. 3.
    Borel, A., Hirzebruch, F.: Characteristic classes and homogeneous spaces I. Am. J. of Math.80, 459–538 (1958)Google Scholar
  4. 4.
    Bott, R., Samelson, H.: Applications of Morse theory to symmetric spaces. Am. J. of Math.80, 964–1029 (1958)Google Scholar
  5. 5.
    Bott, R.: The stable homotopy of the classical groups. Ann. of Math.70, 313–337Google Scholar
  6. 6.
    Eliasson, H.: Morse theory for closed curves. In: Symp for inf. dim. Topology, Lousiana State University. Ann. of Math. Studies No. 69, 63–77. Princeton University Press 1972Google Scholar
  7. 7.
    Eliasson, H.: Über die Anzahl geschlossener Geodätischer in gewissen Riemannschen Mannigfaltigkeiten. Math. Ann.166, 119–147 (1966)Google Scholar
  8. 8.
    Flaschel, P., Klingenberg, W.: Riemannsche Hilbertmannigfaltigkeiten Periodische Geodätische. Lecture Notes in Math. 282. Berlin-Heidelberg-New York: Springer 1972Google Scholar
  9. 9.
    Gromoll, D., Meyer, W.: Periodic geodesics on compact riemannian manifolds. J. of Diff. Geom.3, 493–510 (1969)Google Scholar
  10. 10.
    Klein, P.: Über die Kohomologie des freien Schleifenraumes. Bonner Math. Schriften 55. Bonn: Math. Institut 1972Google Scholar
  11. 11.
    Klingenberg, W.: The space of closed curves on the sphere. Topology7, 395–415 (1968)Google Scholar
  12. 12.
    Klingenberg, W.: The space of closed curves on a projective space. Quart. J. Math. Oxford Ser. 20 No. 77, 11–31 (1969)Google Scholar
  13. 13.
    Klingenberg, W.: Lectures on closed geodesics. Preprint Bonn 1975Google Scholar
  14. 14.
    Loos, O.: Symmetric spaces II. New York: Benjamin 1969Google Scholar
  15. 15.
    Švarc, A.S.: Homology of the space of closed curves. Trudy Moscow. Mat. Obsc.9, 3–44 (1960)Google Scholar
  16. 16.
    Vigué, M., Sullivan, D.: The homology theory of the closed geodesic problem. Preprint Orsay and bures-sur-Yvette, 1975. To appear in J. of Diff. Geom.Google Scholar
  17. 17.
    Wolf, J.A.: Spaces of constant curvature. New York-Toronto-London: McGraw-Hill 1967Google Scholar
  18. 18.
    Ziller, W.: Geschlossene Geodätische auf global symmetrischen und homogenen Räumen. Dissertation, Bonn 1975Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Wolfgang Ziller
    • 1
  1. 1.Mathematisches Institut der Universität BonnBonn

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