Log in :: RSS/Atom Feeds
Bulletin of the American Mathematical Society

Infinite loop space theory

J. P. May
Source: Bull. Amer. Math. Soc. Volume 83, Number 4 (1977), 456-494.
First Page: Show Hide
Primary Subjects: 55–02, 55B20, 55D35, 55F40
Secondary Subjects: 55B15, 55D40, 55E50, 55F50, 18C15, 18D10, 18F25, 18H10
Full-text: Open access
PDF File (4944 KB)
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.bams/1183538891
Mathematical Reviews number (MathSciNet): MR0451235
Zentralblatt MATH identifier: 0357.55016

References

1. J. F. Adams, On the groups J (X). I-IV, Topology 2 (1963), 181-195; ibid. 3 (1965). 137-171; ibid. 3 (1965), 193-222; ibid. 5 (1966), 21-71. MR 28 #2553; 33 #6626, 6627, 6628.
Mathematical Reviews (MathSciNet): MR159336
Digital Object Identifier: doi:10.1016/0040-9383(63)90001-6
2. J. F. Adams, Lectures on generalized cohomology, Category Theory, Homology Theory and Their Applications, III (Battelle Inst. Conf., Seattle, Wash., 1968, Vol. Three), Lecture Notes in Math., vol. 99, Springer, Berlin, 1969, pp. 1-138. MR 40 #4943.
Zentralblatt MATH: 0193.51702
Mathematical Reviews (MathSciNet): MR251716
3. J. F. Adams and S. B. Priddy, Uniqueness of BSO, Proc. Cambridge Philos. Soc. (to appear).
Zentralblatt MATH: 0338.55011
4. D. W. Anderson, Simplicial K-theory and generalized homology theories (preprint).
5. D. W. Anderson, There are no phantom cohomology operations in K-theory (preprint).
Zentralblatt MATH: 0551.55012
Mathematical Reviews (MathSciNet): MR705749
Project Euclid: euclid.pjm/1102720577
6. D. W. Anderson and L. Hodgkin, The K-theory of Eilenberg-Mac Lane complexes, Topology 7 (1968), 317-329. MR 37 #6924.
Zentralblatt MATH: 0199.26302
Mathematical Reviews (MathSciNet): MR231369
Digital Object Identifier: doi:10.1016/0040-9383(68)90009-8
7. S. Araki and T. Kudo, Topology of Hn-spaces and H-squaring operations, Mem. Fac. Sci. Kyūsyū Univ. Ser. A 10 (1956), 85-120. MR 19, 442.
Zentralblatt MATH: 0074.38502
Mathematical Reviews (MathSciNet): MR87948
Digital Object Identifier: doi:10.2206/kyushumfs.10.85
8. E. Artin, Theory of braids, Ann. of Math. (2) 48 (1947), 101-126. MR 8, 367.
Zentralblatt MATH: 0030.17703
Mathematical Reviews (MathSciNet): MR19087
Digital Object Identifier: doi:10.2307/1969218
9. M. F. Atiyah, R. Bott and A. Shapiro, Clifford modules, Topology 3 (1964), suppl. 1, 3-38. MR 29 #5250.
Zentralblatt MATH: 0146.19001
Mathematical Reviews (MathSciNet): MR167985
Digital Object Identifier: doi:10.1016/0040-9383(64)90003-5
10. M. G. Barratt, A free group functor for stable homotopy, Proc. Sympos. Pure Math., Vol. 22, Amer. Math. Soc., Providence, R. I., 1971, pp. 31-35. MR 48 #3043.
Zentralblatt MATH: 0242.55015
Mathematical Reviews (MathSciNet): MR324693
11. M. G. Barratt and P. J. Eccles, Γ+-structures. I-III, Topology 13 (1974), 25-45; ibid. 13 (1974), 113-126; ibid. 13 (1974), 199-207. MR 50 # 1234a, b, c.
Zentralblatt MATH: 0304.55010
12. J. Beck, On H-spaces and infinite loop spaces, Category Theory, Homology Theory and Their Applications, III (Battelle Inst. Conf., Seattle, Wash., 1968, Vol. Three), Lecture Notes in Math., vol. 99, Springer, Berlin, 1969, pp. 139-153. MR 40 #2079.
Zentralblatt MATH: 0198.56003
Mathematical Reviews (MathSciNet): MR248829
13. J. M. Boardman and R. M. Vogt, Homotopy-everything H-spaces, Bull. Amer. Math. Soc. 74 (1968), 1117-1122. MR 38 #5215.
Zentralblatt MATH: 0165.26204
Mathematical Reviews (MathSciNet): MR236922
Digital Object Identifier: doi:10.1090/S0002-9904-1968-12070-1
Project Euclid: euclid.bams/1183530111
14. J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Math., vol. 347, Springer, New York, 1973.
Zentralblatt MATH: 0285.55012
Mathematical Reviews (MathSciNet): MR420609
15. A. K. Bousfield and D. M. Kan, Homotopy limits, completions, and localizations, Lecture Notes in Math., vol. 304, Springer-Verlag, Berlin and New York, 1972. MR 51 #1825.
Zentralblatt MATH: 0259.55004
Mathematical Reviews (MathSciNet): MR365573
16. W. Browder, Homology operations and loop spaces, Illinois J. Math. 4 (1960), 347-357. MR 22 #11395.
Zentralblatt MATH: 0107.40404
Mathematical Reviews (MathSciNet): MR120646
Project Euclid: euclid.ijm/1255456051
17. W. Browder, Surgery on simply-connected manifolds, Ergebnisse math. Grenzgebiete, Bd. 65, Springer-Verlag, New York, 1972. MR 50 #11272.
Zentralblatt MATH: 0239.57016
Mathematical Reviews (MathSciNet): MR358813
18. G. Brumfiel, I. Madsen and R. J. Milgram, PL characteristic classes and cobordism, Ann. of Math. (2) 97 (1973), 82-159. MR 46 #9979.
Zentralblatt MATH: 0248.57006
Mathematical Reviews (MathSciNet): MR310881
Digital Object Identifier: doi:10.2307/1970878
19. F. Cohen, Splitting certain suspensions via self-maps. Illinois J. Math. (to appear).
Zentralblatt MATH: 0316.55008
Mathematical Reviews (MathSciNet): MR405412
Project Euclid: euclid.ijm/1256049904
20. F. Cohen, T. Lada and J. P. May, The homology of iterated loop spaces, Lecture Notes in Math. vol. 533, Springer-Verlag, Berlin and New York, 1976.
Zentralblatt MATH: 0334.55009
Mathematical Reviews (MathSciNet): MR436146
21. E. B. Curtis, The Dyer-Lashof algebra and the ∧-algebra, Illinois J. Math. 19 (1975), 231-246.
Zentralblatt MATH: 0311.55007
Mathematical Reviews (MathSciNet): MR377885
Project Euclid: euclid.ijm/1256050812
22. E. Dyer and R. K. Lashof, Homology of iterated loop spaces, Amer. J. Math. 84 (1962), 35-88. MR 25 #4523.
Zentralblatt MATH: 0119.18206
Mathematical Reviews (MathSciNet): MR141112
Digital Object Identifier: doi:10.2307/2372804
23. E. Fadell and L. Neuwirth, Configuration spaces, Math. Scand. 10 (1962), 111-118. MR 25 #4537.
Zentralblatt MATH: 0136.44104
Mathematical Reviews (MathSciNet): MR141126
24. Z. Fiedorowicz and S. Priddy, Loop spaces and finite orthogonal groups, Bull. Amer. Math. Soc. 81 (1975), 700-702. MR 51 #11487.
Zentralblatt MATH: 0306.55012
Mathematical Reviews (MathSciNet): MR375291
Digital Object Identifier: doi:10.1090/S0002-9904-1975-13827-4
Project Euclid: euclid.bams/1183537139
25. M. Herrero, Homology operations on H*( BU × Z) and H*( BO × Z) related to the tensor product of vector bundles, Thesis, Univ. of Chicago, 1972.
26. L. Hodgkin, The K-theory of some well-known spaces. I: QS0, Topology 11 (1972), 371-375. MR 48 #9701.
Zentralblatt MATH: 0246.55003
Mathematical Reviews (MathSciNet): MR331367
Digital Object Identifier: doi:10.1016/0040-9383(72)90032-8
27. L. Hodgkin and V. P. Snaith, The K-theory of some more well-known spaces (preprint).
Zentralblatt MATH: 0386.55008
28. J. R. Isbell, On coherent algebras and strict algebras, J. Algebra 13 (1969), 299-307. MR 40 #2729.
Zentralblatt MATH: 0181.31503
Mathematical Reviews (MathSciNet): MR249484
Digital Object Identifier: doi:10.1016/0021-8693(69)90076-3
29. L. Jones, Patch spaces: a geometric representation for Poincaré spaces, Ann. of Math. (2) 97 (1973), 276-306. MR 47 #4269.
Zentralblatt MATH: 0263.57003
Mathematical Reviews (MathSciNet): MR315720
Digital Object Identifier: doi:10.2307/1970849
30. D. S. Kahn, Cup-i products and the Adams spectral sequence, Topology 9 (1970), 1-9. MR 40 #6552.
Zentralblatt MATH: 0193.23503
Mathematical Reviews (MathSciNet): MR253337
Digital Object Identifier: doi:10.1016/0040-9383(70)90043-1
31. D. S. Kahn, Homology of the Barratt-Eccles decomposition maps, Notas de Matematicas y Simposià, No 1., Soc. Mat. Mexicana, 1975.
Zentralblatt MATH: 0337.55012
Mathematical Reviews (MathSciNet): MR761721
32. D. S. Kahn and S. B. Priddy, Applications of the transfer to stable homotopy theory, Bull. Amer. Math. Soc. 78 (1972), 981-987. MR 46 #8220.
Zentralblatt MATH: 0265.55009
Mathematical Reviews (MathSciNet): MR309109
Digital Object Identifier: doi:10.1090/S0002-9904-1972-13076-3
Project Euclid: euclid.bams/1183534135
33. S. O. Kochman, Homology of the classical groups over the Dyer-Lashof algebra, Trans. Amer. Math. Soc. 185 (1973), 83-136. MR 48 #9719.
Zentralblatt MATH: 0271.57013
Mathematical Reviews (MathSciNet): MR331386
Digital Object Identifier: doi:10.1090/S0002-9947-1973-0331386-2
34. M. Laplaza, Coherence for distributivity, Coherence in Categories, Lecture Notes in Math., vol. 281, Springer, Berlin, 1972, pp. 29-65. MR 49 #379a.
Zentralblatt MATH: 0244.18010
Mathematical Reviews (MathSciNet): MR335598
Digital Object Identifier: doi:10.1007/BFb0059555
35. N. Levitt and J. W. Morgan, Transversality structures and P. L. structures on spherical fibrations, Bull. Amer. Math. Soc. 78 (1972), 1064-1068. MR 47 #2602.
Zentralblatt MATH: 0267.55021
Mathematical Reviews (MathSciNet): MR314050
Digital Object Identifier: doi:10.1090/S0002-9904-1972-13112-4
Project Euclid: euclid.bams/1183534153
36. H. J. Ligaard, Infinite loop maps from SF to BO⊗ at the prime 2, Illinois J. Math. (to appear)
Zentralblatt MATH: 0394.55018
Mathematical Reviews (MathSciNet): MR458415
Project Euclid: euclid.ijm/1256048932
37. S. Mac Lane, Categorical algebra, Bull. Amer. Math. Soc. 71 (1965), 40-106. MR 30 #2053.
Zentralblatt MATH: 0161.01601
Mathematical Reviews (MathSciNet): MR171826
Digital Object Identifier: doi:10.1090/S0002-9904-1965-11234-4
Project Euclid: euclid.bams/1183526392
38. I. Madsen, On the action of the Dyer-Lashof algebra in H*(G) and H*(G/Top), Thesis, Univ. of Chicago, 1970.
Zentralblatt MATH: 0313.55018
Mathematical Reviews (MathSciNet): MR2611651
39. I. Madsen, On the action of the Dyer-Lashof algebra in H*(G), Pacific J. Math. 60 (1975), 235-275.
Zentralblatt MATH: 0313.55018
Mathematical Reviews (MathSciNet): MR388392
Project Euclid: euclid.pjm/1102868451
40. I. Madsen, Higher torsion in SG and BSG, Math. Z. 143 (1975), 55-80. MR 51 #11503.
Zentralblatt MATH: 0322.55030
Mathematical Reviews (MathSciNet): MR375307
Digital Object Identifier: doi:10.1007/BF01173051
41. I. Madsen and R. J. Milgram, The universal smooth surgery class, Comment. Math. Helv. 50 (1975), 281-310.
Zentralblatt MATH: 0328.55011
Mathematical Reviews (MathSciNet): MR383404
Digital Object Identifier: doi:10.1007/BF02565752
42. I. Madsen, V. P. Snaith and J. Tornehave, Infinite loop maps in geometric topology, Math. Proc. Cambridge Philos. Soc. (to appear).
Zentralblatt MATH: 0357.55015
Mathematical Reviews (MathSciNet): MR494076
Digital Object Identifier: doi:10.1017/S0305004100053482
43. J. P. May, A general algebraic approach to Steenrod operations. The Steenrod Algebra and Its Applications (Proc. Conf., Battelle Memorial Inst., Columbus, Ohio, 1970), Lecture Notes in Math., vol. 168, Springer, Berlin, 1970, pp. 153-231. MR 43 #6915.
Zentralblatt MATH: 0242.55023
Mathematical Reviews (MathSciNet): MR281196
44. J. P. May, Homology operations on infinite loop spaces, Proc. Sympos. Pure. Math., Vol. 22, Amer. Math. Soc. Providence, R. I., 1971. pp. 171-185. MR 47 #7740.
Zentralblatt MATH: 0242.55020
Mathematical Reviews (MathSciNet): MR319195
45. J. P. May, The geometry of iterated loop spaces, Lecture Notes in Math. Vol. 271, Springer, New York, 1972.
Zentralblatt MATH: 0244.55009
Mathematical Reviews (MathSciNet): MR420610
46. J. P. May, E∞ spaces, group completions, and permutative categories, New Developments in Topology (Proc. Sympos. Algebraic Topology, Oxford, 1972), London Math. Soc. Lecture Note Ser., no. 11, Cambridge Univ. Press, London, 1974, pp. 61-93. MR 49 #3915.
Zentralblatt MATH: 0281.55003
Mathematical Reviews (MathSciNet): MR339152
47. J. P. May, Classifying spaces and fibrations, Mem. Amer. Math. Soc. 1 (1975), issue 1, no. 155. MR 51 #6806.
Zentralblatt MATH: 0321.55033
Mathematical Reviews (MathSciNet): MR370579
48. J. P. May, (with contributions by F. Quinn, N. Ray and J. Tornehave), E∞ ring spaces and E∞ ring spectra, Lecture Notes in Math., vol 577, Springer-Verlag, Berlin and New York, 1977.
Zentralblatt MATH: 0345.55007
Mathematical Reviews (MathSciNet): MR494077
49. J. P. May, The homotopical foundations of algebraic topology, Monograph London Math. Soc., Academic Press, London (in preparation).
50. R. J. Milgram, Iterated loop spaces, Ann. of Math. (2) 84 (1966), 386-403. MR 34 #6767.
Zentralblatt MATH: 0145.19901
Mathematical Reviews (MathSciNet): MR206951
Digital Object Identifier: doi:10.2307/1970453
51. R. J. Milgram, The mod 2 spherical characteristic classes, Ann. of Math. (2) 92 (1970), 238-261. MR 41 #7705.
Zentralblatt MATH: 0208.51601
Mathematical Reviews (MathSciNet): MR263100
Digital Object Identifier: doi:10.2307/1970836
52. R. J. Milgram, Group representations and the Adams spectral sequence, Pacific J. Math. 41 (1972), 157-182. MR 46 #3598.
Zentralblatt MATH: 0264.55010
Mathematical Reviews (MathSciNet): MR304463
Project Euclid: euclid.pjm/1102968426
53. R. J. Milgram, Unstable homotopy from the stable point of view, Lecture Notes in Math., vol. 368, Springer-Verlag, Berlin and New York, 1974. MR 50 #1235.
Zentralblatt MATH: 0274.55015
Mathematical Reviews (MathSciNet): MR348740
54. D. Moore, On homology operations for the classifying spaces of certain groups, Thesis, Northwestern Univ., Evanston, Ill., 1974.
Mathematical Reviews (MathSciNet): MR2624438
55. M. Nakaoka, Decomposition theorem for homology groups of symmetric groups, Ann. of Math. (2) 71 (1960), 16-42. MR 22 #2989.
Zentralblatt MATH: 0090.39002
Mathematical Reviews (MathSciNet): MR112134
Digital Object Identifier: doi:10.2307/1969878
56. M. Nakaoka, Homology of the infinite symmetric group, Ann. of Math. (2) 73 (1961), 229-257. MR 24 #A1721.
Zentralblatt MATH: 0099.25301
Mathematical Reviews (MathSciNet): MR131874
Digital Object Identifier: doi:10.2307/1970333
57. G. Nishida, Cohomology operations in iterated loop spaces, Proc. Japan Acad. 44 (1968), 104-109. MR 39 #2156.
Zentralblatt MATH: 0165.26202
Mathematical Reviews (MathSciNet): MR240811
Digital Object Identifier: doi:10.3792/pja/1195521291
Project Euclid: euclid.pja/1195521291
58. G. Nishida, The nilpotency of elements of the stable homotopy groups of spheres, J. Math. Soc. Japan 25 (1973), 707-732. MR 49 #6236.
Zentralblatt MATH: 0261.55013
Mathematical Reviews (MathSciNet): MR341485
Digital Object Identifier: doi:10.2969/jmsj/02540707
Project Euclid: euclid.jmsj/1240435467
59. F. P. Peterson, The Mod p homotopy type of BSO and F/PL, Bol. Soc. Mat. Mexicana (2) 14 (1969), 22-27. MR 41 #4540.
Zentralblatt MATH: 0189.54403
Mathematical Reviews (MathSciNet): MR259911
60. S. B. Priddy, Dyer-Lashof operations for the classifying spaces of certain matrix groups, Quart. J. Math. Oxford Ser. (2) 26 (1975), no. 102, 179-193. MR 51 #11505.
Zentralblatt MATH: 0311.55013
Mathematical Reviews (MathSciNet): MR375309
Digital Object Identifier: doi:10.1093/qmath/26.1.179
61. D. Quillen, The Adams conjecture, Topology 10 (1970), 67-80. MR 43 #5525.
Zentralblatt MATH: 0219.55013
Mathematical Reviews (MathSciNet): MR279804
Digital Object Identifier: doi:10.1016/0040-9383(71)90018-8
62. D. Quillen, On the cohomology and K-theory of the general linear groups over a finite field, Ann. of Math. (2) 96 (1972), 552-586. MR 47 #3565.
Zentralblatt MATH: 0249.18022
Mathematical Reviews (MathSciNet): MR315016
Digital Object Identifier: doi:10.2307/1970825
63. D. Quillen, Higher K-theory for categories with exact sequences, New Developments in Topology (Proc. Sympos. Algebraic Topology, Oxford, 1972), London Math. Soc. Lecture Note Ser., no. 11, Cambridge Univ. Press, London, 1974, pp. 95-103. MR 49 #384.
Zentralblatt MATH: 0276.18013
Mathematical Reviews (MathSciNet): MR335604
64. D. Quillen, Higher algebraic K-theory. I, Algebraic K-Theory. I: Higher K-Theories (Proc. Conf. Seattle Res. Center, Battelle Memorial Inst., 1972), Lecture Notes in Math., vol. 341, Springer, Berlin, 1973, pp. 85-147. MR 49 #2895.
Zentralblatt MATH: 0292.18004
Mathematical Reviews (MathSciNet): MR338129
65. F. Quinn, Surgery on Poincare and normal spaces, Bull. Amer. Math. Soc. 78 (1972), 262-267. MR 45 #6014.
Zentralblatt MATH: 0233.57007
Mathematical Reviews (MathSciNet): MR296955
Digital Object Identifier: doi:10.1090/S0002-9904-1972-12950-1
Project Euclid: euclid.bams/1183533487
66. G. Segal, Configuration-spaces and iterated loop-spaces, Invent. Math. 21 (1973), 213-221. MR 48 #9710.
Zentralblatt MATH: 0267.55020
Mathematical Reviews (MathSciNet): MR331377
Digital Object Identifier: doi:10.1007/BF01390197
67. G. Segal, Categories and cohomology theories, Topology 13 (1974), 293-312. MR 50 #5782.
Zentralblatt MATH: 0284.55016
Mathematical Reviews (MathSciNet): MR353298
Digital Object Identifier: doi:10.1016/0040-9383(74)90022-6
68. J.-P. Serre, Cohomologie modulo 2 des complexes d'Eilenberg-Mac Lane, Comment. Math. Helv. 27 (1953), 198-232. MR 15, 643.
Zentralblatt MATH: 0052.19501
Mathematical Reviews (MathSciNet): MR60234
Digital Object Identifier: doi:10.1007/BF02564562
69. V. P. Snaith, A stable decomposition of ΩnSnX, J. London Math. Soc. (2) 7 (1974), 577-583, MR 49 #3918.
Zentralblatt MATH: 0275.55019
Mathematical Reviews (MathSciNet): MR339155
Digital Object Identifier: doi:10.1112/jlms/s2-7.4.577
70. V. P. Snaith, Dyer-Lashof operations in K-theory, Lecture Notes in Math., vol. 496, Springer, New York, 1975, pp. 103-294.
Mathematical Reviews (MathSciNet): MR394662
Zentralblatt MATH: 0323.55009
71. J. D. Stasheff, Homotopy associativity of H-spaces. I, II, Trans. Amer. Math. Soc. 108 (1963), 275-312. MR 28 #1623.
Zentralblatt MATH: 0114.39402
Mathematical Reviews (MathSciNet): MR158400
72. N. E. Steenrod (Notes, rev. by D.B.A. Epstein), Cohomology operations, Ann. of Math. Studies, no. 50, Princeton Univ. Press, Princeton, N. J., 1962. MR 26 #3056.
Zentralblatt MATH: 0102.38104
Mathematical Reviews (MathSciNet): MR145525
73. D. Sullivan, Geometric topology seminar, Princeton University (mimeographed notes).
74. D. Sullivan, Geometric topology. I: Localization, periodicity, and Galois symmetry, M.I.T. (mimeographed notes).
Zentralblatt MATH: 1078.55001
75. D. Sullivan, Genetics of homotopy theory and the Adams conjecture, Ann. of Math. (2) 100 (1974), 1-79.
Zentralblatt MATH: 0355.57007
Mathematical Reviews (MathSciNet): MR442930
Digital Object Identifier: doi:10.2307/1970841
76. E. Thomas, The generalized Pontrjagin cohomology operations and rings with divided powers, Mem. Amer. Math. Soc. No. 27 (1957), 82 pp. MR 20 #5474.
Zentralblatt MATH: 0085.37504
Mathematical Reviews (MathSciNet): MR99029
77. J. Tornehave, Delooping the Quillen map, Thesis, M.I.T., 1971.
78. J. Tornehave, On BSG and the symmetric groups (preprint).
79. J. Tornehave, On the splitting of spherical fibration theory at odd primes (preprint).
80. A. Tsuchiya, Characteristic classes for spherical fiber spaces, Nagoya Math. J. 43 (1971), 1-39. MR 45 #7736.
Zentralblatt MATH: 0237.55015
Mathematical Reviews (MathSciNet): MR298687
Project Euclid: euclid.nmj/1118798364
81. A. Tsuchiya, Characteristic classes for PL micro bundles, Nagoya Math. J. 43 (1971), 169-198. MR 47 #2614.
Zentralblatt MATH: 0238.55013
Mathematical Reviews (MathSciNet): MR314062
Project Euclid: euclid.nmj/1118798375
82. A. Tsuchiya, Homology operations on ring spectrum of H∞ type and their applications, J. Math. Soc. Japan 25 (1973), 277-316. MR 47 #4255.
Zentralblatt MATH: 0262.55018
Mathematical Reviews (MathSciNet): MR315706
Digital Object Identifier: doi:10.2969/jmsj/02520277
Project Euclid: euclid.jmsj/1240435670

2013 © American Mathematical Society

Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

Turn MathJax Off
What is MathJax?