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Infinite loop space theory revisited

  • D. Loop and H. Spaces
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Algebraic Topology Waterloo 1978

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 741))

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Bibliography

  1. J. F. Adams. Infinite loop spaces. Annals of Math. Studies No. 90. Princeton. 1978.

    Google Scholar 

  2. J. C. Becker. Characteristic classes and K-theory. Springer Lecture Notes in Mathematics Vol. 428, pp. 132–143. 1974.

    Article  Google Scholar 

  3. J. M. Boardman and R. M. Vogt. Homotopy Invariant Algebraic Structures on Topological Spaces. Springer Lecture Notes in Mathematics Vol. 347. 1973.

    Google Scholar 

  4. R. Bruner. The Adams spectral sequence of H∞ ring spectra. Thesis. Univ. of Chicago. 1977.

    Google Scholar 

  5. R. Bruner, G. Lewis, J. P. May, J. McClure, and M. Steinberger. H∞ Ring Spectra and their Applications. Springer Lecture Notes in Mathematics. In preparation.

    Google Scholar 

  6. G. Brumfiel and I. Madsen. Evaluation of the transfer and the universal surgery classes. Inventiones math. 32 (1976), 133–169.

    Article  MathSciNet  MATH  Google Scholar 

  7. F. R. Cohen. Braid orientations and bundles with flat connections. Inventiones math. 46 (1978), 99–110.

    Article  MATH  Google Scholar 

  8. F. R. Cohen, T. Lada, and J. P. May. The Homology of Iterated Loop Spaces. Springer Lecture Notes in Mathematics Vol. 533. 1976.

    Google Scholar 

  9. F. R. Cohen, J. P. May, and L. R. Taylor. Splitting of certain spaces CX. Math. Proc. Camb. Phil. Soc. to appear.

    Google Scholar 

  10. E. B. Curtis. The Dyer-Lashof algebra and the Λ-algebra. Ill. J. Math. 19 (1975), 231–246.

    MathSciNet  MATH  Google Scholar 

  11. T. tom Dieck. Faserbündel mit Gruppenoperation. Archiv der Math. 20 (1969), 136–143.

    Article  MATH  Google Scholar 

  12. Z. Fiedorowicz. A note on the spectra of algebraic K-theory, Topology 16 (1977), 417–422.

    Article  MathSciNet  MATH  Google Scholar 

  13. Z. Fiedorowicz. The Quillen-Grothendieck construction and extensions of pairings. Springer Lecture Notes in Mathematics Vol. 657, 163–169. 1978.

    Article  MathSciNet  Google Scholar 

  14. Z. Fiedorowicz. The primary components of the Im J spaces. Manuscript, 1978.

    Google Scholar 

  15. Z. Fiedorowicz and S. B. Priddy. Homology of Classical Groups over Finite Fields and their Associated Infinite Loop Spaces. Springer Lecture Notes in Mathematics Vol. 674. 1978.

    Google Scholar 

  16. E. Friedlander. The infinite loop Adams conjecture. Math. Proc. Camb. Phil. Soc. To appear. (Manuscript, 1978).

    Google Scholar 

  17. E. Friedlander and R. Seymour. Two proofs of the stable Adams conjecture. Bull. Amer. Math. Soc. 83 (1977), 1300–1302.

    Article  MathSciNet  MATH  Google Scholar 

  18. J. W. Gray. Closed categories, lax limits and homotopy limits. Preprint, 1978.

    Google Scholar 

  19. A. Hatcher. Higher simple homotopy theory. Annals of Math. 102 (1975), 101–137.

    Article  MathSciNet  MATH  Google Scholar 

  20. H. Hauschild. Zerspaltung äquivariante Homotopiemengen. Math. Ann. 230 (1977), 279–292.

    Article  MathSciNet  MATH  Google Scholar 

  21. H. Hauschild. Klassifizierende Räume, G-Konfigurationsräume und und äquivariante Schleifenräume. Manuscript, 1978.

    Google Scholar 

  22. L. Hodgkin. The K-theory of some well-known spaces I, QS0. Topology 11 (1972), 371–375.

    Article  MathSciNet  MATH  Google Scholar 

  23. L. Hodgkin and V. P. Snaith. The K-theory of some more well-known spaces. Ill. J. Math. 22 (1978), 270–278.

    MathSciNet  MATH  Google Scholar 

  24. D. S. Kahn and S. B. Priddy. On the transfer in the homology of symmetric groups. Math. Proc. Camb. Phil. Soc. 83 (1978), 91–101.

    Article  MathSciNet  MATH  Google Scholar 

  25. D. S. Kahn and S. B. Priddy. The transfer and stable homotopy theory. Math. Proc. Camb. Phil. Soc. 83 (1978), 103–111.

    Article  MathSciNet  MATH  Google Scholar 

  26. D. Kraines and T. Lada. A counterexample to the transfer conjecture. These proceedings.

    Google Scholar 

  27. R. Lashof and M. Rothenberg. G smoothing theory. Proc. Symp. Pure Math. Vol. 32, part I, pp. 211–266. Amer. Math. Soc. 1978.

    Article  MathSciNet  Google Scholar 

  28. G. Lewis, The stable category and generalized Thom spectra. Thesis. Univ. of Chicago. 1978.

    Google Scholar 

  29. H. Ligaard. On the spectral sequence for π*(MSTop). Thesis. Univ. of Chicago. 1976.

    Google Scholar 

  30. H. Ligaard and J. P. May. On the Adams spectral sequence for π*MSTop, I. Preprint, 1976.

    Google Scholar 

  31. I. Madsen. Remarks on normal invariants from the infinite loop space viewpoint. Proc. Symposia Pure Math. Vol. 32, part I, pp. 91–102. Amer. Math. Soc. 1978.

    Article  MathSciNet  Google Scholar 

  32. I. Madsen, V. P. Snaith, and J. Tornehave. Infinite loop maps in geometric topology. Math. Proc. Camb. Phil. Soc. 81 (1977), 399–430.

    Article  MathSciNet  MATH  Google Scholar 

  33. B. Mann and R. J. Milgram. On the action of the Steenrod algebra on H*(MSPL) at odd primes. Preprint, 1976.

    Google Scholar 

  34. T. Matumota. On G-CW complexes and a theorem of J.H.C. Whitehead. J. Fac. Sci. Tokyo 18 (1971–72), 363–374.

    Google Scholar 

  35. J. P. May. The Geometry of Iterated Loop Spaces. Springer Lecture Notes in Mathematics Vol. 271. 1972.

    Google Scholar 

  36. J. P. May (with contributions by F. Quinn, N. Ray, and J. Tornehave). E∞ Ring Spaces and E∞ Ring Spectra. Springer Lecture Notes in Mathematics Vol. 577. 1977.

    Google Scholar 

  37. J. P. May. Infinite loop space theory. Bull. Amer. Math. Soc. 83 (1977), 456–494.

    Article  MathSciNet  MATH  Google Scholar 

  38. J. P. May. A∞ ring spaces and algebraic K-theory. Springer Lecture Notes in Mathematics Vol. 658, 240–315. 1978.

    Article  Google Scholar 

  39. J. P. May. H∞ ring spectra and their applications. Proc. Symp. Pure Math. Vol. 32, part 2, pp. 229–244. Amer. Math. Soc. 1978.

    Article  Google Scholar 

  40. J. P. May. The spectra associated to permutative categories. Topology. To appear.

    Google Scholar 

  41. J. P. May. The spectra associated to l-monoids. Math. Proc. Camb. Phil. Soc. To appear.

    Google Scholar 

  42. J. P. May. Applications and generalizations of the approximation theorem. Proc. conf. in Algebraic Topology. Aarhus. 1978.

    Google Scholar 

  43. J. P. May and R. Thomason. The uniqueness of infinite loop space machines. Topology. To appear.

    Google Scholar 

  44. J. McClure. H ∞d* ring spectra and their cohomology operations. Thesis. Univ. of Chicago. 1978.

    Google Scholar 

  45. H. R. Miller. A spectral sequence for the homology of an infinite delooping. Preprint, 1977.

    Google Scholar 

  46. H. R. Miller and S. B. Priddy. On G and the stable Adams conjecture. Springer Lecture Notes in Mathematics Vol. 658, 331–348, 1978.

    Article  MathSciNet  Google Scholar 

  47. S. B. Priddy. Homotopy splittings involving G and G/O. Comm. Math. Helv. 53 (1978), 470–484.

    Article  MathSciNet  MATH  Google Scholar 

  48. G. Segal. Equivariant K-theory. Publ. Math. I.H.E.S. Vol. 34 (1968), 129–151.

    MATH  Google Scholar 

  49. G. Segal. The stable homotopy of complex projective space. Quart. J. Math. Oxford (2) 24 (1973), 1–5.

    Article  MATH  Google Scholar 

  50. G. Segal. Categories and cohomology theories. Topology 13 (1974), 293–312.

    Article  MathSciNet  MATH  Google Scholar 

  51. G. Segal. The multiplicative group of classical cohomology. Quart. J. Math. Oxford (3) 26 (1975), 289–293.

    Article  MATH  Google Scholar 

  52. G. Segal. Power operations in stable homotopy theory. Preprint.

    Google Scholar 

  53. G. Segal. Some results in equivariant homotopy theory. Manuscript, 1978.

    Google Scholar 

  54. R. M. Seymour. Vector bundles invariant under the Adams operations. Quart. J. Math. Oxford (2) 25 (1974), 395–414.

    Article  MathSciNet  MATH  Google Scholar 

  55. V. P. Snaith. Dyer-Lashof operations in K-theory. Springer Lecture Notes in Mathematics Vol. 496, 103–294. 1975.

    Article  MathSciNet  Google Scholar 

  56. V. P. Snaith. The complex J-homomorphism. I. Proc. London Math. Soc. (3) 34 (1977), 269–302.

    Article  MathSciNet  MATH  Google Scholar 

  57. V. P. Snaith. The 2-primary J-homomorphism. Math. Proc. Camb. Phil. Soc. 82 (1977), 381–387.

    Article  MathSciNet  MATH  Google Scholar 

  58. V. P. Snaith. The total Chern and Stiefel-Whitney classes are not infinite loop maps. Illinois J. Math. 21 (1977), 300–304.

    MathSciNet  MATH  Google Scholar 

  59. V. P. Snaith. Algebraic cobordism and K-theory. Memoir Amer. Math. Soc. To appear.

    Google Scholar 

  60. M. Steinberger. Homology operations for H∞ ring spectra. Thesis. Univ. of Chicago. 1977.

    Google Scholar 

  61. R. J. Steiner. Thesis. Cambridge Univ. 1977.

    Google Scholar 

  62. R. J. Steiner. Spectra and products of Eilenberg-Mac Lane spaces. Preprint, 1978.

    Google Scholar 

  63. R. Street. Two constructions on lax functors. Cahiers de Topologie et Geometrie Differentielle 13 (1972), 217–264.

    MathSciNet  MATH  Google Scholar 

  64. R. Thomason. Homotopy colimits in the category of small categories. Preprint, 1977.

    Google Scholar 

  65. R. Thomason. First quadrant spectral sequences in algebraic K-theory. Preprint, 1978.

    Google Scholar 

  66. R. Thomason. Uniqueness of delooping machines. Preprint, 1978.

    Google Scholar 

  67. J. Tornehave. Deviation from additivity of a solution to the Adams conjecture. To appear.

    Google Scholar 

  68. F. Waldhausen. Algebraic K-theory of topological spaces, I. Proc. Symp. Pure Math. Vol. 32, part 1, pp. 35–60. Amer. Math. Soc. 1978.

    Article  MathSciNet  Google Scholar 

  69. S. Waner. Equivariant classifying spaces and fibrations. Thesis. Univ. of Chicago. 1978.

    Google Scholar 

  70. S. Waner. Equivariant infinite loop spaces. Manuscript, 1978.

    Google Scholar 

  71. R. Wellington. The A-algebra H* Ω n+10 Σn+1X, the Dyer-Lashof algebra, and the Λ-algebra. Thesis. Univ. of Chicago. 1977.

    Google Scholar 

  72. R. Woolfson. Hyper-Γ-spaces and hyperspectra. Preprint, 1978.

    Google Scholar 

  73. R. Woolfson. Γ-spaces, orientations and cohomology operations. Preprint, 1978.

    Google Scholar 

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Authors
  1. J. P. May
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Editors and Affiliations

  1. Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

    Peter Hoffman

  2. Department of Mathematics, University of Western Ontario, London, Ontario, Canada, N6A 5B9

    Victor Snaith

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© 1979 Springer-Verlag Berlin Heidelberg

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May, J.P. (1979). Infinite loop space theory revisited. In: Hoffman, P., Snaith, V. (eds) Algebraic Topology Waterloo 1978. Lecture Notes in Mathematics, vol 741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062160

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  • DOI: https://doi.org/10.1007/BFb0062160

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  • Print ISBN: 978-3-540-09545-3

  • Online ISBN: 978-3-540-35009-5

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