Characteristic numbers and group actions

Transformation Groups
Part of the Lecture Notes in Mathematics book series (LNM, volume 1474)


Vector Bundle Cobordism Class Surgery Obstruction Homotopy Sphere Finite Group Action 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Asd]
    A. Assadi, Finite Group Actions on Simply Connected Manifolds and CW Complexes, Memoirs Amer. Math. Soc. 257 (1982).Google Scholar
  2. [AS]
    M. F. Atiyah and I. M. Singer, The index of elliptic operators, III,Ann. of Math 87 (1968), 546–604.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [AW]
    J. F. Adams and G. Walker, On complex Stiefel manifolds, Proc.Camb. Phil.Soc. 61 (1965), 81–103.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [B]
    A. Bak, Odd dimensional surgery groups of odd torsion groups vanish, Topology 14 (1975), 367–374.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [BP]
    W. Browder and T. Petrie, Diffeomorphisms of manifolds and semifree actions on homotopy spheres, Bull. Amer. Math. Soc. 77 (1971), 160–163.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [tD]
    T. tom Dieck, Bordism of G-manifolds and integrality theorems, Topology 9 (1970), 345–358.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [DP1]
    K. H. Dovermann and T. Petrie, G-Surgery II, Memoirs Amer. Math. Soc. 260 (1982).Google Scholar
  8. [DP2]
    _____, An induction theorem for equivariant surgery (G-Surgery III), Amer.J.Math. 105 (1983), 1369–1403.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [DP3]
    _____, Smith equivalence for representations of odd order groups, Topology 24 (1985), 283–305.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [DR1]
    K. H. Dovermann and M. Rothenberg, An equivariant surgery sequence and equivariant homeomorphism and diffeomorphism classification, Topology Symposium (Siegen, 1979), Lecture Notes in Math. Vol. 788, Springer, Berlin-HeidelbergNew York-Toyko, 1980, pp. 257–280.zbMATHGoogle Scholar
  11. [DR2]
    _____, Equivariant Surgery and Classification of Finite Group Actions on Manifolds, Memoirs Amer. Math. Soc. 379 (1988).Google Scholar
  12. [E]
    J. Ewing, Spheres as fixed point sets, Quart.J.Math.Oxford 27 (1976), 445–455.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [H1]
    F. Hirzebruch, Topological Methods in Algebraic Geometry, Spinger-Verlag, new York, 1966.CrossRefzbMATHGoogle Scholar
  14. [H2]
    _____, Hilbert modular surfaces, L'enseignement mathematique 19 (1973), 183–281.MathSciNetzbMATHGoogle Scholar
  15. [J]
    L. Jones, The converse to the fixed point theorem of P. A. Smith II, Indiana Univ. Math. J. 22 (1972), 309–325 correction 24 (1975), 1001–1003.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [Kaw]
    K. Kawakubo, The index and the Todd genus ofp-actions, Amer. J. Math. 97 (1975), 182–204.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [K]
    S.S. Kim, Ph.D. Thesis, Purdue University,1988.Google Scholar
  18. [KM]
    M. Kervaire and J. Milnor, Groups of homotopy spheres, Ann. of Math. 77 (1963), 504–537.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [MS]
    M. Masuda and R. Schultz, Equivariant inertia groups and rational invariants for nonfree actions (to appear).Google Scholar
  20. [O]
    R. Oliver, Fixed point sets of finite group actions on acyclic complexes, Comment. Math. Helv. 50 (1975), 155–177.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [Pa1]
    K. Pawalowski, Fixed points of cyclic group actions on disks, Bull. Acad. Polon. Sci. Math. Astr. Phys. 26 (1978), 1011–1015.MathSciNetzbMATHGoogle Scholar
  22. [Pa2]
    _____, Group actions with inequivalent representations at fixed points, Math.Z. 187 (1984), 29–47.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [Pa3]
    _____, Equivariant thickening for compact Lie group actions, Mathematica Gottingensis 71 (1986).Google Scholar
  24. [Pa4]
    _____, Fixed points of smooth group actions on disks and euclidean spaces, preprint, 1986.Google Scholar
  25. [S]
    R. Stong, Notes on Corbordism Theory, Mathematical Notes, Princeton University Press, 1968.Google Scholar
  26. [ST]
    I. N. Stewart and D. O. Tall, Algebraic Number Theory (second edition), Champman and Hall, New York, 1987.zbMATHGoogle Scholar
  27. [S1]
    R. Schultz, Nonlinear analogs of linear group actions on spheres, Bull. Amer.Math. Soc 11 (1984), 263–285.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [S2]
    _____, Pontryagin numbers and periodic diffeomorphisms of spheres, to appear in the Proceedings of the Conference on Group Actions, Osaka, 1987 (in the Springer Lecture Notes Series).Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  1. 1.Department of MathematicsPaichai UniversityTaejonKorea

Personalised recommendations