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Upper bounds for the toral symmetry of certain homotopy spheres

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Algebraic Topology Aarhus 1982

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1051))

Partially supported by NSF Grant MCS 81-04852

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References

  1. M. Atiyah and G. Segal, Equivariant K-theory and completion, J. Diff. Geom. 3 (1969), 1–18.

    MathSciNet  MATH  Google Scholar 

  2. M. F. Atiyah and I. M. Singer, The index of elliptic operators III, Ann. of Math. 87(1968), 546–604.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. C. Becker and R. E. Schultz, Equivariant function spaces and stable homotopy theory I, Comment. Math. Helv. 49(1974), 1–34.

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Borel (ed.), Seminar on Transformation Groups, Ann. of Math. Studies No. 46. Princeton University Press, Princeton, 1960.

    Google Scholar 

  5. G. Bredon, Exotic actions on spheres, Proc. Conf. on Transformation Groups (New Orleans, 1967), 47–76. Springer, New York, 1968.

    Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  7. W. C. Hsiang and W. Y. Hsiang, Differentiable actions of compact connected classical groups I, Amer. J. Math. 89(1967), 705–786.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  9. Kh. Knapp, Rank and Adams filtrations of a Lie group, Topology 17(1978), 41–52.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  11. L. N. Mann, Differentiable actions of compact abelian Lie groups on Sn, Proc. Amer. Math. Soc. 16(1965), 480–484.

    MathSciNet  MATH  Google Scholar 

  12. J. P. May, J. E. McClure, and G. V. Triantaffillou, The construction of equivariant localizations, Bull. London Math. Soc. 14(1982), 223–230.

    Article  MathSciNet  Google Scholar 

  13. P. S. Mostert (ed.), Problems, Proc. Conf. on Transformation Groups (New Orleans, 1967), p. 235. Springer, New York, 1968.

    Google Scholar 

  14. R. Schultz, Semifree circle actions and the degree of symmetry of homotopy spheres, Amer. J. Math. 93(1971), 829–839.

    Article  MathSciNet  MATH  Google Scholar 

  15. —, Circle actions on homotopy spheres bounding generalized plumbing manifolds, Math. Ann. 205(1973), 201–210.

    Article  MathSciNet  MATH  Google Scholar 

  16. —, Differentiable group actions on homotopy spheres: I. Differential structure and the knot invariant, Invent. Math. 31(1975), 103–128.

    MathSciNet  MATH  Google Scholar 

  17. —, ibid, Trans. Amer. Math. Soc. 268(1981), 255–297.

    MathSciNet  MATH  Google Scholar 

  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.

    MATH  Google Scholar 

  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. —, Almost isovariant homotopy smoothings of compact G-manifolds, to appear (summarized in pre-preprint, Purdue, 1976).

    Google Scholar 

  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. S. Stolz, On homotopy spheres bounding highly connected manifolds, to appear.

    Google Scholar 

  23. H. Toda, p-primary components of homotopy groups. III. Stable groups of the sphere, Mem. College Sci. Univ. Kyoto 31(1958), 191–210.

    MathSciNet  MATH  Google Scholar 

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Ib H. Madsen Robert A. Oliver

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© 1984 Springer-Verlag

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Schultz, R. (1984). Upper bounds for the toral symmetry of certain homotopy spheres. In: Madsen, I.H., Oliver, R.A. (eds) Algebraic Topology Aarhus 1982. Lecture Notes in Mathematics, vol 1051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075594

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  • DOI: https://doi.org/10.1007/BFb0075594

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