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Equivariant function spaces and stable homotopy theory I

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Commentarii Mathematici Helvetici

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References

  1. Adams, J. F.,On the groups J(X)-IV, Topology5 (1966), 21–80.

    Article  MathSciNet  Google Scholar 

  2. Atiyah, M. F.,Thom complexes, Proc. London Math. Soc.11 (1961), 291–310.

    MATH  MathSciNet  Google Scholar 

  3. —,K-theory, Benjamin, New York, 1967.

    Google Scholar 

  4. Becker, J. C.,On the existence of A k -structures on stable vector bundles, Topology9, (1970), 367–384.

    Article  MATH  MathSciNet  Google Scholar 

  5. —,Vector fields on quotient manifolds of spheres, Indiana Univ. Math. Jour.22 (1973), 859–871.

    Article  MATH  Google Scholar 

  6. Boardman, J. M.,Stable homotopy theory, Chapter V—Duality and Thom Spectra, mimeographed. University of Warwick, 1966.

  7. Bott, R.,The stable homotopy of the classical groups, Ann. of Math.70 (1959), 313–337.

    Article  MathSciNet  Google Scholar 

  8. Browder, W.,Surgery and the theory of differentiable transformation groups, Proc. of the Conf. of Transformation Groups (New Orleans, 1967), 1–46. Springer-Verlag, New York, 1968.

    Google Scholar 

  9. Conner, P. andFloyd, E.,The relation of cobordism to K-theories, Lecture Notes in Mathematics28, Springer-Verlag, New York, 1966.

    MATH  Google Scholar 

  10. Dold, A. andLashof, R.,Quasifibrations and fibre homotopy equivalence of bundles, Ill. J. Math.3, (1959), 285–305.

    MATH  MathSciNet  Google Scholar 

  11. Gleason, A.,Spaces with a compact lie group of transformations, Proc. Amer. Math. Soc.1 (1950), 35–43.

    Article  MATH  MathSciNet  Google Scholar 

  12. James, I. M.,Spaces associated with Stiefel manifolds, Proc. London Math. Soc.9, (1959), 115–140.

    MATH  MathSciNet  Google Scholar 

  13. —,The space of bundle maps, Topology2, (1963), 45–59.

    Article  MATH  MathSciNet  Google Scholar 

  14. —,Bundles with special structure—I, Ann. Math.89, (1969), 359–390.

    Article  Google Scholar 

  15. —,Ex-homotopy theory—I, Ill. Jour. Math.15, (1971), 324–337.

    MATH  Google Scholar 

  16. Kahn, D. S. andPriddy, S. B.,Applications of the transfer to stable homotopy theory, to appear.

  17. Lee, R.,The spherical space form problem, Topology12 (1973).

  18. May, J. P.,The geometry of iterated loop spaces, Lecture Notes in Mathematics271, Springer-Verlag, New York, 1972.

    MATH  Google Scholar 

  19. Milnor, J.,On spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc.90 (1959), 272–280.

    Article  MathSciNet  Google Scholar 

  20. Milnor, J.,Lectures on characteristic classes, mimeographed, Princeton University, 1957.

  21. Mosher, R. andTangora, M.,Cohomology operations and applications in homotopy theory, Harper and Row, New York, 1968.

    MATH  Google Scholar 

  22. Petrie, T.,Free metacyclic group actions on spheres, Ann. of Math.94, (1971), 108–124.

    Article  MathSciNet  Google Scholar 

  23. Roush, F. W.,Transfer in generalized cohomology theories, Thesis, Princeton University, 1971.

  24. Schultz, R. E.,Homotopy decompositions of equivariant function spaces—I, Math. Zeitschrift131 (1973), 49–75; ibid.Schultz, R. E. Homotopy decompositions of equivariant function spaces—II, Math. Zeitschrift132 (1973), 69–90.

    Article  MATH  MathSciNet  Google Scholar 

  25. Segal, G.,Equivariant stable homotopy theory, Actes, Congrès internat. math. (Nice, 1970) T. 2, 59–63, Gauthier-Villars, Paris, 1971.

    Google Scholar 

  26. Spanier, E. H.,Algebraic topology, McGraw-Hill, New York, 1966.

    MATH  Google Scholar 

  27. Stasheff, J.,A classification theorem for fibre spaces, Topology2 (1963), 239–246.

    Article  MATH  MathSciNet  Google Scholar 

  28. Szczarba, R.,On tangent bundles of fibre spaces and quotient spaces, Amer. J. Math.86, (1964), 685–697.

    Article  MATH  MathSciNet  Google Scholar 

  29. Tom Dieck, Tammo,Faserbündel mit Gruppenoperation, Arch. Math. (Basel)20, (1969), 136–143.

    MATH  MathSciNet  Google Scholar 

  30. Tsuchiya, A.,Characteristic classes for spherical fiber spaces, Nagoya Math. J.43, (1971), 1–39.

    MATH  MathSciNet  Google Scholar 

  31. Vogt, R. Boardman’s stable homotopy category, mimeographed, Aarhus University, 1970.

  32. Whitehead, G. W.,On products in homotopy groups, Ann. of Math.47, (1946), 460–475.

    Article  MathSciNet  Google Scholar 

  33. Wu Wen-Tsün,On Pontrjagin classes—II (Chinese), Acta Math. Sinica4, (1954), 171–199. English translation, Amer. Math. Soc. Translations (2)92 (1970), 63–92.

    MATH  MathSciNet  Google Scholar 

  34. Yang, C. T.,The triangulability of the orbit space of a differentiable transformation group, Bull., Amer. Math. Soc.69, (1963), 405–408.

    Article  MATH  MathSciNet  Google Scholar 

  35. Schultz, R.,Homotopy sphere pairs admitting semifree differentiable actions, Amer. J. Math., to appear.

  36. Schultz, R. Homotopy-theoretic restrictions for smooth actions on exotic spheres, to appear.

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Authors and Affiliations

  1. Division of Math. Sci., Purdue University, Lafayette, Ind.

    J. C. Becker & R. E. Schultz

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  1. J. C. Becker
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  2. R. E. Schultz
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Partially supported by NSF Grant GP-34197

Partially supported by NSF Grant GP-19530

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Becker, J.C., Schultz, R.E. Equivariant function spaces and stable homotopy theory I. Commentarii Mathematici Helvetici 49, 1–34 (1974). https://doi.org/10.1007/BF02566716

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