Upper bounds for the toral symmetry of certain homotopy spheres

  • Reinhard Schultz
Transformation Groups
Part of the Lecture Notes in Mathematics book series (LNM, volume 1051)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Atiyah and G. Segal, Equivariant K-theory and completion, J. Diff. Geom. 3 (1969), 1–18.MathSciNetMATHGoogle Scholar
  2. 2.
    M. F. Atiyah and I. M. Singer, The index of elliptic operators III, Ann. of Math. 87(1968), 546–604.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    J. C. Becker and R. E. Schultz, Equivariant function spaces and stable homotopy theory I, Comment. Math. Helv. 49(1974), 1–34.MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    A. Borel (ed.), Seminar on Transformation Groups, Ann. of Math. Studies No. 46. Princeton University Press, Princeton, 1960.Google Scholar
  5. 5.
    G. Bredon, Exotic actions on spheres, Proc. Conf. on Transformation Groups (New Orleans, 1967), 47–76. Springer, New York, 1968.Google Scholar
  6. 6.
    M. Davis, W. C. Hsiang, and W. Y. Hsiang, Differential actions of compact simple Lie groups on homotopy spheres and Euclidean spaces, Proc. A.M.S. Sympos. Pure Math 32 Pt. 1 (1978), 313–323.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    W. C. Hsiang and W. Y. Hsiang, Differentiable actions of compact connected classical groups I, Amer. J. Math. 89(1967), 705–786.MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    W. Y. Hsiang, On the unknottedness of the fixed point set of differentiable circle group actions on spheres — P. A. Smith conjecture, Bull. Amer. Math. Soc. 70 (1964), 678–680.MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Kh. Knapp, Rank and Adams filtrations of a Lie group, Topology 17(1978), 41–52.MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    H. B. Lawson and S.-T. Yau, Scalar curvature, nonabelian group actions, and the degree of symmetry of exotic spheres, Comment. Math. Helv. 49(1974), 232–244.MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    L. N. Mann, Differentiable actions of compact abelian Lie groups on Sn, Proc. Amer. Math. Soc. 16(1965), 480–484.MathSciNetMATHGoogle Scholar
  12. 12.
    J. P. May, J. E. McClure, and G. V. Triantaffillou, The construction of equivariant localizations, Bull. London Math. Soc. 14(1982), 223–230.MathSciNetCrossRefGoogle Scholar
  13. 13.
    P. S. Mostert (ed.), Problems, Proc. Conf. on Transformation Groups (New Orleans, 1967), p. 235. Springer, New York, 1968.Google Scholar
  14. 14.
    R. Schultz, Semifree circle actions and the degree of symmetry of homotopy spheres, Amer. J. Math. 93(1971), 829–839.MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    —, Circle actions on homotopy spheres bounding generalized plumbing manifolds, Math. Ann. 205(1973), 201–210.MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    —, Differentiable group actions on homotopy spheres: I. Differential structure and the knot invariant, Invent. Math. 31(1975), 103–128.MathSciNetMATHGoogle Scholar
  17. 17.
    —, ibid, Trans. Amer. Math. Soc. 268(1981), 255–297.MathSciNetMATHGoogle Scholar
  18. 18.
    —, Spherelike G-manifolds with exotic equivariant tangent bundles, Studies in Alg. Top. (Adv. in Math. Suppl. Studies Vol. 5), 1–39. Academic Press, New York, 1979.MATHGoogle Scholar
  19. 19.
    —, Exotic spheres admitting circle actions with codimension 4 fixed point sets, Conference on Homotopy (Northwestern, 1982), Contemporary Mathematics (A.M.S. Series), to appear.Google Scholar
  20. 20.
    —, Almost isovariant homotopy smoothings of compact G-manifolds, to appear (summarized in pre-preprint, Purdue, 1976).Google Scholar
  21. 21.
    —, Differentiability and the P. A. Smith theorems for spheres: I, Current Trends in Algebraic Topology (Conference, London, Ont., 1981), C.M.S. Conf. Proc. 2 Pt. 2, (1982), 235–273.Google Scholar
  22. 22.
    S. Stolz, On homotopy spheres bounding highly connected manifolds, to appear.Google Scholar
  23. 23.
    H. Toda, p-primary components of homotopy groups. III. Stable groups of the sphere, Mem. College Sci. Univ. Kyoto 31(1958), 191–210.MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Reinhard Schultz
    • 1
  1. 1.Purdue UniversityWest Lafayette

Personalised recommendations