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manuscripta mathematica

, Volume 12, Issue 4, pp 307–327 | Cite as

Bordismengruppen unitärer Torusmannigfaltigkeiten

  • Peter Löffler
Article

Abstract

Let G be a k-dimensional torus. Let U * G , denote the homotopical unitary bordism theory. We show that restriction to the fixed point set determines an element of U * G . This implies that the bordism class of a unitary G-manifold is determined by its characteristic numbers in equivariant K-theory.

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Literatur

  1. 1.
    J.C. Alexander: The bordism ring of manifolds with involution, Proceeding of the AMS, 31, 536–542 (1972)Google Scholar
  2. 2.
    M.F. Atiyah: Characters and cohomology of finite groups, Publ. Ist. Hautes Etudes Sci. 9, 23–64 (1961)Google Scholar
  3. 3.
    Th. Bröcker - T. tom Dieck: Kobordismentheorie, Lecture Notes in Math. 178, Springer 1970Google Scholar
  4. 4.
    Th. Bröcker -E. C. Hooks: Stable equivariant bordism, Math. Z. 129, 269–277 (1972)Google Scholar
  5. 5.
    P.E. Conner - E.E. Floyd: Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 33, Springer-Verlag, 1964Google Scholar
  6. 6.
    P.E. Conner -E.E. Floyd: Maps of odd period, Ann. of Math. 84, 132–156 (1966)Google Scholar
  7. 7.
    T. tom Dieck: Faserbündel mit Gruppenoperation, Arch. Math. 17, 395–399 (1969)Google Scholar
  8. 8.
    T. tom Dieck: Kobordismentheorie und Transformationsgruppen, Preprint Series 1968/69, Math. Inst., Aarhus Univ.Google Scholar
  9. 9.
    T. tom Dieck: Bordism of G-manifolds and integrality theorems, Topology 9, 345–358 (1970)Google Scholar
  10. 10.
    T. tom Dieck: Lokalisierung äquivarianter Kohomologietheorien, Math. Z. 121, 253–262 (1971)Google Scholar
  11. 11.
    T. tom Dieck: Periodische Abbildungen unitärer Mannigfaltigkeiten, Math. Z. 126, 275–295 (1972)Google Scholar
  12. 12.
    T. tom Dieck: Bemerkungen über äquivarianten Eulerklassen, Proc. of the second conf. on compact transformation groups I, Lecture Notes in Math 298, 152–162 (1972)Google Scholar
  13. 13.
    T. tom Dieck: Orbittypen und äquivariante Homologie I, Arch. Math. 23, 307–317 (1972)Google Scholar
  14. 14.
    G. Hamrick -E. Ossa: Unitary bordism of monogenic groups and isometries, Proc. Conf. on compact transformation groups, Lecture Notes in Math. 298, 172–182 (1972)Google Scholar
  15. 15.
    P.S. Landweber: A note on cobordism of classifying spaces, Math. Scand 29 (1971)Google Scholar
  16. 16.
    P. Löffler: Dissertation, Saarbrücken 1973Google Scholar
  17. 17.
    P. Löffler: Equivariant unitary cobordism and completion, Budva 1972Google Scholar
  18. 18.
    E. Ossa: Fixpunkfreie S1-Operationen, Math. Ann. 186, 42–52 (1970)Google Scholar
  19. 19.
    R. E. Strong: Unoriented bordism and actions of finite groups, Mem. of AMS 103 (1970)Google Scholar
  20. 20.
    E. Ossa: Unitary bordism of abelian groups, Proceedings of the AMS 33, 568–571 (1972)Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Peter Löffler
    • 1
  1. 1.Mathematisches Institut der Universität des Saarlandes

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