Mathematische Zeitschrift

, Volume 201, Issue 2, pp 279–302 | Cite as

On the equivariant morse chain complex of the space of closed curves

  • Hans-Bert Rademacher


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [A1]
    Anosov, D.V.: Certain homotopies in the space of closed curves. Izv. Akad. Nauk SSSR44, 1219–1254 (1980) (Russian)=Math. USSR Izv.17, 423–353 (1981)Google Scholar
  2. [A2]
    Anosov, D.V.: Some homology classes in the space of closed curves in then-dimensional sphere. Izv. Akad. Nauk SSSR45, 467–490 (1981) (Russian)=Math. USSR Izv.18, 403–422 (1982)Google Scholar
  3. [Ba]
    Ballmann, W.: Über geschlossene Geodätische. Habilitationschrift. Univ. Bonn 1983Google Scholar
  4. [Br]
    Bredon, G.: Introduction to compact transformation groups. New York, London: Academic Press 1972Google Scholar
  5. [Hi]
    Hingston, N.: Equivariant morse theory and closed geodesics. J. Differ. Geom.19, 85–116 (1984)Google Scholar
  6. [I1]
    Illman, S.: Equivariant singular homology and cohomology for actions of compact Lie groups. Proc. of 2nd. conf. on cpt. transf. groups. Springer Lect. Notes Math.298, 401–415 (1972)Google Scholar
  7. [I2]
    Illman, S.: Equivariant algebraic topology. Thesis. Princeton Univ. 1972Google Scholar
  8. [K1]
    Klingenberg, W.: Lectures on closed geodesics. Grundlehren Math. Wiss.230. Berlin Heidelberg New York: Springer 1978Google Scholar
  9. [K2]
    Klingenberg, W.: Closed geodesics on Riemannian manifolds. Conf. board of the math. sciences. Reg. conf. series in math. 53. Amer. Math. Soc. Providence 1983Google Scholar
  10. [Ma1]
    Matumoto, T.: EquivariantK-theory and Fredholm operators. J. Fac. Sci. Univ. Tokyo Sect. IA18, 109–112 (1971)Google Scholar
  11. [Ma2]
    Matumoto, T.: OnG-CW complexes and a theorem of J.H.C. Whitehead. J. Fac. Sci. Univ. Tokyo Sect. IA18, 363–374 (1971)Google Scholar
  12. [M1]
    Milnor, J.: Morse theory (3rd ed.) Ann. Math. Studies 51. Princeton: Univ. Press 1969Google Scholar
  13. [M2]
    Milnor, J.: Lectures on theh-cobordism theorem. Princeton Math. Notes. Princeton: Univ. Press 1965Google Scholar
  14. [Pe]
    Peng, X.W.: On the Morse complex. Math. Z.187, 86–96 (1984)Google Scholar
  15. [R1]
    Rademacher, H.B.: Der Äquivariante Morse-Kettenkomplex des Raums der geschlossenen Kurven. Bonner Math. Schriften178 (1987)Google Scholar
  16. [R2]
    Rademacher, H.B.: On the average indices of closed geodesics. To appear in: J. Differ. Geom.28 (1988)Google Scholar
  17. [Sp]
    Spanier, E.: Algebraic topology. New York: McGraw Hill 1966Google Scholar
  18. [Sv]
    Svarc, A.S.: Homology of the space of closed curves. Trudy Moskov Math. Obsc.9, 3–44 (1960) (Russian)Google Scholar
  19. [Wo]
    Wolter, T.: Der Morsekomplex für nicht-degenerierte kritische Untermannigfaltigkeiten. Diplomarbeit. Univ. Bonn 1986Google Scholar
  20. [Zi]
    Ziller, W.: The free loop space of globally symmetric spaces. Invent. Math.41, 1–22 (1977)Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Hans-Bert Rademacher
    • 1
  1. 1.Mathematisches Institut der Universität BonnBonn 1Germany

Personalised recommendations