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Bulletin of the American Mathematical Society

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Finite dimensional $H$-spaces


Author: Morton Curtis
Journal: Bull. Amer. Math. Soc. 77 (1971), 1-12
MSC (1970): Primary 55D45; Secondary 55F10, 57F25
DOI: https://doi.org/10.1090/S0002-9904-1971-12599-5
Addendum to finite dimensional $H$-spaces: Bull. Amer. Math. Soc., Volume 77, Number 6 (1971), 1120--1120
MathSciNet review: 0278303
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  • 1. J. F. Adams, Vector fields on spheres, Ann. of Math. (2) 75 (1962), 603-632. MR 25 #2614. MR 139178
  • 2. J. F. Adams, H-spaces with few cells, Topology 1 (1962), 67-72. MR 26 #5574. MR 148065
  • 3. J. F. Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. (2) 72 (1960), 20-104. MR 25 #4530. MR 141119
  • 4. J. F. Adams, The sphere, considered as an H-space mod p, Quart, J. Math. Oxford Ser. (2) 12 (1962), 52-60. MR 23 #A651. MR 123323
  • 5. S. Araki, I. M. James and E. Thomas, Homotopyabelian Lie groups, Bull. Amer. Soc. 66 (1960), 324-326. MR 22 #9973. MR 119207
  • 6. M. F. Atiyah, Power operations in K-theory, Quart. J. Math. Oxford Ser (2) 17 (1966), 165-193. MR 34 #2004. MR 202130
  • 7. M. F. Atiyah and F. Hirzebruch, Vector bundles and homogeneous spaces, Proc Sympos. Pure Math., vol. 3, Amer. Math. Soc., Providence, R. I., 1961, pp. 7-38. MR 25 #2617. MR 139181
  • 8. Paul F. Baum and W. Browder, The cohomology of quotients of classical groups, Topology 3 (1965), 305-336. MR 32 #6490. MR 189063
  • 9. J. M. Boardman and R. M. Vogt, Homotopy-everything H-spaces, Bull. Amer. Math. Soc. 74 (1968), 1117-1122. MR 38 #5215. MR 236922
  • 10. A. Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groups de Lie compacts, Ann. of Math. (2) 57 (1953), 115-207. MR 14, 490. MR 51508
  • 11. R. Bott, A report on the unitary group, Proc. Sympos. Pure Math., vol. 3, Amer. Math. Soc., Providence, R. I., 1961, pp. 1-6. MR 24 #A2393. MR 132553
  • 12. R. Bott, The stable homotopy of the classical groups, Ann. of Math. (2) 70 (1959), 313-337. MR 22 #987. MR 110104
  • 13. W. Browder, Homology operations and loop spaces, Illinois J. Math. 4 (1960), 347-357. MR 22 #11395. MR 120646
  • 14. W. Browder, Higher torsion in H-spaces, Trans. Amer. Math. Soc. 108 (1963), 353-375. MR 27 #5260. MR 155326
  • 15. W. Browder, Homotopy commutative H-spaces, Ann. of Math. (2) 75 (1962), 283-311. MR 27 #765. MR 150778
  • 16. W. Browder, The cohomology of covering spaces of H-spaces, Bull. Amer. Math. Soc. 65 (1959), 140-141. MR 22 #1891. MR 111024
  • 17. W. Browder, Torsion in H-spaces, Ann. of Math. (2) 74 (1961), 24-51. MR 23 #A2201. MR 124891
  • 18. W. Browder, Loop spaces of H-spaces, Bull. Amer. Math. Soc. 66 (1960), 316-319. MR 22 #8508. MR 117733
  • 19. W. Browder and Edwin Spanier, H-spaces and duality, Pacific J. Math. 12 (1962), 411-414. MR 26 #1891. MR 144346
  • 20. W. Browder and Emery Thomas, On the projective plane of an H-space, Illinois J. Math. 7 (1963), 492-502. MR 27 #1955. MR 151974
  • 21. Robert F. Brown, H-manifolds have no nontrivial idempotents, U.C.L.A., 1969 (preprint). MR 239584
  • 22. Robert F. Brown, Divisible H-spaces, U.C.L.A., 1969 (preprint). MR 261594
  • 23. Allan, Clark, On π3 of finite dimensional H-spaces, Ann. of Math. (2) 78 (1963), 193-196. MR 27 #1956.
  • 24. Allan, Clark, Hopf algebras over Dedekind domains and torsion in H-spaces, Brown University, Providence, R. I. (preprint). MR 189026
  • 25. A. H. Copeland, Jr., On H-spaces with two non-trivial homotopy groups, Proc. Amer. Math. Soc. 8 (1957), 184-191. MR 18, 754. MR 83737
  • 26. C. R. Curjel and P. R. Douglas, On H-spaces of finite dimension, (preprint). MR 341479
  • 27. Morton Curtis and Guido Mislin, H-spaces which are bundles over S7, Rice University, Houston, Tex., 1969 (preprint). MR 286102
  • 28. A. Dold and R. Lashof, Principal quasi-fibrations and fibre homotopy equivalence of bundles, Illinois J. Math. 3 (1959), 285-305. MR 21 #331. MR 101521
  • 29. R. R. Douglas, Homotopy-commutativity in H-spaces, Quart. J. Math. Oxford Ser. (2) 18 (1967), 263-283. MR 36 #3347. MR 220281
  • 30. R. R. Douglas and F. Sigrist, Sphere bundles over spheres which are H-spaces, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 44 (1968), 502-505. MR 38 #5211. MR 236918
  • 31. R. R. Douglas, P. Hilton and F. Sigrist, H-spaces, Lecture Notes in Math., no. 92, Springer-Verlag, Berlin and New York, 1969, pp. 65-73. MR 250304
  • 32. R. R. Douglas and F. Sigrist, Homotopy-associative H-spaces which are sphere bundles over spheres, Comment. Math. Helv. 44 (1969), 308-309. MR 40 #2071. MR 248821
  • 33. R. R. Douglas and F. Sigrist, Sphere bundles over spheres and H-spaces, Topology 8 (1969), 115-118. MR 39 #6312. MR 244999
  • 34. E. Halpern, Twisted polynomial hyperalgebras, Mem. Amer. Math. Soc. No. 29 (1958). MR 21 #2982. MR 104225
  • 35. P. J. Hilton, Note on a theorem of Stasheff, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 127-130. MR 25 #4536. MR 141125
  • 36. P. J. Hilton and J. Roitberg, On principal S3-bundles over spheres, Ann. of Math. (2) 90 (1969) 91-107. MR 39 #7624. MR 246320
  • 37. P. J. Hilton and J. Roitberg, Note on principal S3-bundles, Bull. Amer. Math. Soc. 74 (1968), 957-959. MR 37 #5889. MR 230327
  • 38. H. Hopf, Über die Topologie der Gruppen-Mannigfaltigkeiten und ihre Verallgemeinerungen, Ann. of Math. (2) 42 (1941), 22-52. MR 3, 61. MR 4784
  • 39. J. R. Hubbuck, On homotopy commutative H-spaces, (preprint). MR 238316
  • 40. J. R. Hubbuck, On finitely generated cohomology Hopf algebras, (preprint). MR 261600
  • 41. J. R. Hubbuck, Generalized cohomology operations and H-spaces of low rank, (preprint). MR 248809
  • 42. J. R. Hubbuck, Some results in the theory of H-spaces, Bull. Amer. Math. Soc. 74 (1968), 965-967. MR 37 #4805. MR 229231
  • 43. I. M. James, Commutative products on spheres, Proc. Cambridge Philos. Soc. 53 (1957), 63-68. MR 18, 918. MR 84770
  • 44. I. M. James, The ten types of H-spaces, 1959, (preprint).
  • 45. I. M. James, On Lie groups and their homotopy groups, Proc. Cambridge Philos. Soc. 55 (1959), 244-247. MR 23 #A1371. MR 124051
  • 46. I. M. James, On homotopy-commutativity, Topology 6 (1967), 405-410. MR 35 #3662. MR 212797
  • 47. I. M. James, On spaces with a multiplication, Pacific J. Math. 7 (1957), 1083-1100. MR 19, 876. MR 90813
  • 48. I. M. James, On H-spaces and their homotopy groups, Quart. J. Math. Oxford Ser. (2) 11 (1960), 161-179. MR 24 #A2966. MR 133132
  • 49. I. M. James, Multiplication on spheres. I, Proc. Amer. Math. Soc. 8 (1957), 192-196. MR 18, 752. MR 83726
  • 50. I. M. James, Multiplication on spheres. II, Trans. Amer. Math. Soc. 84 (1957), 545-558. MR 19, 875. MR 90812
  • 51. I. M. James, Products on spheres, Mathematika 6 (1959), 1-13. MR 26 #5576. MR 148067
  • 52. I. M. James, On sphere-bundles. I, Bull. Amer. Math. Soc. 75 (1969), 617-621. MR 39 #3517. MR 242184
  • 53. I. M. James and E. Thomas, Homotopy-abelian topological groups, Topology 1 (1962), 237-240. MR 26 #6970. MR 149483
  • 54. I. M. James and E. Thomas, Which Lie groups are homotopy-abelian? Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 737-740. MR 21 #5197. MR 106465
  • 55. I. M. James, On homotopy-commutativity, Ann. of Math. (2) 76 (1962), 9-17. MR 25 #2603a. MR 139166
  • 56. I. M. James and J. H. C. Whitehead, The homotopy theory of sphere bundles over spheres. II, Proc. London Math. Soc. (3) 5 (1955), 148-166. MR 16, 948. MR 68836
  • 57. I. M. James and J. H. C. Whitehead, The homotopy theory of sphere bundles over spheres. I, Proc. London Math. (3) 4 (1954), 196-218. MR 15, 892. MR 61838
  • 58. M. A. Kervaire, On the Pontryagin classes of certain SO(n)-bundles over manifolds, Amer. J. Math. 80 (1958), 632-638. MR 21 #1592. MR 102806
  • 59. R. J. Milgram, The bar construction and abelian H-spaces, Illinois J. Math. 11 (1967), 242-250. MR 34 #8404. MR 208595
  • 60. J. W. Milnor, and J. C. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211-264. MR 30 #4259. MR 174052
  • 61. John Morgan, Stable tangential homotopy equivalences, Ph.D. Thesis, Rice University, Houston, Tex., 1969.
  • 62. F. P. Peterson, A note on H-spaces, Bol. Soc. Mat. Mexicana (2) 4 (1959), 30-31. MR 22 #11393. MR 120644
  • 63. H. Samelson, Topology of Lie groups, Bull. Amer. Math. Soc. 58 (1952), 2-37. MR 13, 533. MR 45129
  • 64. Hans Scheerer, Homotopieäquivalente kompakte Liesche Gruppen, Topology 7 (1968), 227-232. MR 37 #4833. MR 229259
  • 65. J.-P. Serre, Quelques calculs de groupes d'homotopie, C. R. Acad. Sci. Paris 236 (1953), 2475-2477. MR 14, 1110. MR 55684
  • 66. Larry Smith, On the type of an associative H-space of rank two, Tôhoku Math. J. (2) 20 (1968), 511-515. MR 39 #4844. MR 243523
  • 67. E. H. Spanier and J. H. C. Whitehead, On fibre spaces in which the fibre is contractible, Comment, Math. Helv. 29 (1955), 1-8. MR 16, 610. MR 66646
  • 68. J. D. Stasheff, On homotopy Abelian H-spaces, Proc. Cambridge Philos. Soc. 57 (1961), 734-745. MR 25 #4534. MR 141123
  • 69. J. D. Stasheff, Manifolds of the homotopy type of (non-Lie) groups, Bull. Amer. Math. Soc. 75 (1969), 998-1000. MR 39 #7623. MR 246319
  • 70. J. D. Stasheff, Homotopy associativity of H-spaces. I, II, Trans. Amer. Math. Soc. 108 (1963), 275-312. MR 28 #1623. MR 158400
  • 71. M. Sugawara, A condition that a space is an H-space, Math. J. Okayama Univ. 6 (1957), 109-129. MR 19, 160. MR 86303
  • 72. M. Sugawara, A condition that a space is group-like, Math. J. Okayama Univ. 7 (1957), 123-149. MR 20 #3546. MR 97066
  • 73. M. Sugawara, On the homotopy-commulativity of groups and loop spaces, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math. 33 (1960/61), 257-269. MR 22 #11394. MR 120645
  • 74. M. Sugawara, Some remarks on homotopy equivalences and H-spaces, Math. J. Okayama Univ. 8 (1958), 125-131. MR 21 #2981. MR 104224
  • 75. Emery Thomas, Steenrod squares and H-spaces, Ann. of Math. (2) 77 (1963), 306-317. MR 26 #3057. MR 145526
  • 76. Emery Thomas, Steenrod squares and H-spaces. II, Ann. of Math. (2) 81 (1965), 473-495. MR 31 #1671. MR 177408
  • 77. Emery Thomas, The Steenrod squares in the mod two cohomology algebra of an H-space, Colloque de Topologie, (Brussels, 1964), Librairie Universitaire, Louvain, 1966, pp. 113-117. MR 36 #3342. MR 220276
  • 78. H. Toda, Generalized Whitehead products and homotopy groups of spheres, J. Inst. Polytech. Osaka City Univ. Ser. A. Math. 3 (1952), 43-82. MR 15, 732. MR 60822
  • 79. H. Toda, Composition methods in homotopy groups of spheres, Ann. of Math. Studies, no. 49, Princeton Univ. Press, Princeton, N. J., 1962. MR 26 #777. MR 143217
  • 80. G. W. Whitehead, Note on a theorem of Sugawara, Bol. Soc. Mat. Mexicana (2) 4 (1959), 33-41. MR 23 #A648. MR 123320
  • 81. G. W. Whitehead, On mappings into group-like spaces, Comment. Math. Helv. 28 (1954), 320-328. MR 16, 505. MR 65927
  • 82. A. Zabrodsky, Implications in the cohomology of H-spaces, (mimeograph).
  • 83. A. Zabrodsky, Homotopy associativity and finite CW complexes, University of Illinois, Chicago Circle, Urbana, Ill. (mimeograph).
  • 84. A. Zabrodsky, The classification of simply connected H-spaces with three cells, (to appear).

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DOI: https://doi.org/10.1090/S0002-9904-1971-12599-5

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