Finite dimensional $H$-spaces
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- Bull. Amer. Math. Soc. 77 (1971), 1-12
References
- J. F. Adams, Vector fields on spheres, Ann. of Math. (2) 75 (1962), 603–632. MR 139178, DOI 10.2307/1970213
- J. F. Adams, $H$-spaces with few cells, Topology 1 (1962), 67–72. MR 148065, DOI 10.1016/0040-9383(62)90097-6
- J. F. Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. (2) 72 (1960), 20–104. MR 141119, DOI 10.2307/1970147
- J. F. Adams, The sphere, considered as an $H$-space $\textrm {mod}\,p$, Quart. J. Math. Oxford Ser. (2) 12 (1961), 52–60. MR 123323, DOI 10.1093/qmath/12.1.52
- S. Araki, I. M. James, and Emery Thomas, Homotopy-abelian Lie groups, Bull. Amer. Math. Soc. 66 (1960), 324–326. MR 119207, DOI 10.1090/S0002-9904-1960-10487-9
- M. F. Atiyah, Power operations in $K$-theory, Quart. J. Math. Oxford Ser. (2) 17 (1966), 165–193. MR 202130, DOI 10.1093/qmath/17.1.165
- M. F. Atiyah and F. Hirzebruch, Vector bundles and homogeneous spaces, Proc. Sympos. Pure Math., Vol. III, American Mathematical Society, Providence, R.I., 1961, pp. 7–38. MR 0139181
- Paul F. Baum and William Browder, The cohomology of quotients of classical groups, Topology 3 (1965), 305–336. MR 189063, DOI 10.1016/0040-9383(65)90001-7
- J. M. Boardman and R. M. Vogt, Homotopy-everything $H$-spaces, Bull. Amer. Math. Soc. 74 (1968), 1117–1122. MR 236922, DOI 10.1090/S0002-9904-1968-12070-1
- Armand Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. (2) 57 (1953), 115–207 (French). MR 51508, DOI 10.2307/1969728
- Raoul Bott, A report on the unitary group, Proc. Sympos. Pure Math., Vol. III, American Mathematical Society, Providence, R.I., 1961, pp. 1–6. MR 0132553
- Raoul Bott, The stable homotopy of the classical groups, Ann. of Math. (2) 70 (1959), 313–337. MR 110104, DOI 10.2307/1970106
- William Browder, Homology operations and loop spaces, Illinois J. Math. 4 (1960), 347–357. MR 120646
- William Browder, Higher torsion in $H$-spaces, Trans. Amer. Math. Soc. 108 (1963), 353–375. MR 155326, DOI 10.1090/S0002-9947-1963-0155326-8
- William Browder, Homotopy commutative $H$-spaces, Ann. of Math. (2) 75 (1962), 283–311. MR 150778, DOI 10.2307/1970175
- William Browder, The cohomology of covering spaces of $H$-spaces, Bull. Amer. Math. Soc. 65 (1959), 140–141. MR 111024, DOI 10.1090/S0002-9904-1959-10299-8
- William Browder, Torsion in $H$-spaces, Ann. of Math. (2) 74 (1961), 24–51. MR 124891, DOI 10.2307/1970305
- William Browder, Loop spaces of $H$-spaces, Bull. Amer. Math. Soc. 66 (1960), 316–319. MR 117733, DOI 10.1090/S0002-9904-1960-10484-3
- William Browder and Edwin Spanier, $H$-spaces and duality, Pacific J. Math. 12 (1962), 411–414. MR 144346, DOI 10.2140/pjm.1962.12.411
- William Browder and Emery Thomas, On the projective plane of an $H$-space, Illinois J. Math. 7 (1963), 492–502. MR 151974
- Robert F. Brown, A fixed point theorem for open $Q$-acyclic $n$-manifolds, Proc. Amer. Math. Soc. 21 (1969), 621–622. MR 239584, DOI 10.1090/S0002-9939-1969-0239584-8
- Robert F. Brown, Divisible $H$-spaces, Proc. Amer. Math. Soc. 26 (1970), 185–189. MR 261594, DOI 10.1090/S0002-9939-1970-0261594-3 23. Allan, Clark, On π3 of finite dimensional H-spaces, Ann. of Math. (2) 78 (1963), 193-196. MR 27 #1956.
- Allan Clark, Hopf algebras over Dedekind domains and torsion in $H$-spaces, Pacific J. Math. 15 (1965), 419–426. MR 189026, DOI 10.2140/pjm.1965.15.419
- Arthur H. Copeland Jr., On $H$-spaces with two non-trivial homotopy groups, Proc. Amer. Math. Soc. 8 (1957), 184–191. MR 83737, DOI 10.1090/S0002-9939-1957-0083737-0
- C. R. Curjel and Roy Douglas, On $H$-spaces of finite dimension, Proceedings of the Advanced Study Institute on Algebraic Topology (Aarhus Univ., Aarhus, 1970) Various Publ. Ser., No. 13, Mat. Inst., Aarhus Univ., Aarhus, 1970, pp. 88–97. MR 0341479
- Morton Curtis and Guido Mislin, $H$-spaces which are bundles over $S^{7}$, J. Pure Appl. Algebra 1 (1971), no. 1, 27–40. MR 286102, DOI 10.1016/0022-4049(71)90010-7
- Albrecht Dold and Richard Lashof, Principal quasi-fibrations and fibre homotopy equivalence of bundles, Illinois J. Math. 3 (1959), 285–305. MR 101521
- Roy R. Douglas, Homotopy-commutativity in $H$-spaces, Quart. J. Math. Oxford Ser. (2) 18 (1967), 263–283. MR 220281, DOI 10.1093/qmath/18.1.263
- Roy R. Douglas, Sphere bundles over spheres which are $H$-spaces, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 44 (1968), 502–505 (English, with Italian summary). MR 236918
- R. R. Douglas, P. J. Hilton, and F. Sigrist, $H$-spaces, Category Theory, Homology Theory and their Applications, II (Battelle Institute Conference, Seattle, Wash., 1968, Vol. Two), Springer, Berlin, 1969, pp. 65–73. MR 0250304
- Roy R. Douglas and François Sigrist, Homotopy-associative $H$-spaces which are sphere bundles over spheres, Comment. Math. Helv. 44 (1969), 308–309. MR 248821, DOI 10.1007/BF02564530
- Roy R. Douglas and François Sigrist, Sphere bundles over spheres and $H$-spaces, Topology 8 (1969), 115–118. MR 244999, DOI 10.1016/0040-9383(69)90003-2
- Edward Halpern, Twisted polynomial hyperalgebras, Mem. Amer. Math. Soc. 29 (1958), 61 pp. (1958). MR 104225
- P. J. Hilton, Note on a theorem of Stasheff, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 127–130. MR 141125
- Peter Hilton and Joseph Roitberg, On principal $S^{3}$-bundles over spheres, Ann. of Math. (2) 90 (1969), 91–107. MR 246320, DOI 10.2307/1970683
- Peter Hilton and Joseph Roitberg, Note on principal $S^{3}$-bundles, Bull. Amer. Math. Soc. 74 (1968), 957–959. MR 230327, DOI 10.1090/S0002-9904-1968-12103-2
- Heinz Hopf, Über die Topologie der Gruppen-Mannigfaltigkeiten und ihre Verallgemeinerungen, Ann. of Math. (2) 42 (1941), 22–52 (German). MR 4784, DOI 10.2307/1968985
- J. R. Hubbuck, On homotopy commutative $H$-spaces, Topology 8 (1969), 119–126. MR 238316, DOI 10.1016/0040-9383(69)90004-4
- J. R. Hubbuck, Finitely generated cohomology Hopf algebras, Topology 9 (1970), 205–210. MR 261600, DOI 10.1016/0040-9383(70)90009-1
- J. R. Hubbuck, Generalized cohomology operations and $H$-spaces of low rank, Trans. Amer. Math. Soc. 141 (1969), 335–360. MR 248809, DOI 10.1090/S0002-9947-1969-0248809-9
- J. R. Hubbuck, Some results in the theory of $H$-spaces, Bull. Amer. Math. Soc. 74 (1968), 965–967. MR 229231, DOI 10.1090/S0002-9904-1968-12105-6
- I. M. James, Commutative products on spheres, Proc. Cambridge Philos. Soc. 53 (1957), 63–68. MR 84770, DOI 10.1017/S0305004100031996 44. I. M. James, The ten types of H-spaces, 1959, (preprint).
- I. M. James, On Lie groups and their homotopy groups, Proc. Cambridge Philos. Soc. 55 (1959), 244–247. MR 124051, DOI 10.1017/s030500410003396x
- I. M. James, On homotopy-commutativity, Topology 6 (1967), 405–410. MR 212797, DOI 10.1016/0040-9383(67)90026-2
- I. M. James, On spaces with a multiplication, Pacific J. Math. 7 (1957), 1083–1100. MR 90813, DOI 10.2140/pjm.1957.7.1083
- I. M. James, On $H$-spaces and their homotopy groups, Quart. J. Math. Oxford Ser. (2) 11 (1960), 161–179. MR 133132, DOI 10.1093/qmath/11.1.161
- I. M. James, Multiplication on spheres. I, Proc. Amer. Math. Soc. 8 (1957), 192–196. MR 83726, DOI 10.1090/S0002-9939-1957-0083726-6
- I. M. James, Multiplication on spheres. II, Trans. Amer. Math. Soc. 84 (1957), 545–558. MR 90812, DOI 10.1090/S0002-9947-1957-0090812-8
- I. M. James, Products on spheres, Mathematika 6 (1959), 1–13. MR 148067, DOI 10.1112/S0025579300001868
- I. M. James, On sphere-bundles. I, Bull. Amer. Math. Soc. 75 (1969), 617–621. MR 242184, DOI 10.1090/S0002-9904-1969-12266-4
- Ioan James and Emery Thomas, Homotopy-abelian topological groups, Topology 1 (1962), 237–240. MR 149483, DOI 10.1016/0040-9383(62)90105-2
- Ioan James and Emery Thomas, Which Lie groups are homotopy-abelian?, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 737–740. MR 106465, DOI 10.1073/pnas.45.5.737
- Ioan James and Emery Thomas, On homotopy-commutativity, Ann. of Math. (2) 76 (1962), 9–17. MR 139166, DOI 10.2307/1970262
- 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 68836, DOI 10.1112/plms/s3-5.2.148
- I. M. James and J. H. C. Whitehead, The homotopy theory of sphere bundles over spheres. I, Proc. London Math. Soc. (3) 4 (1954), 196–218. MR 61838, DOI 10.1112/plms/s3-4.1.196
- Michel A. Kervaire, On the Pontryagin classes of certain $\textrm {SO}(n)$-bundles over manifolds, Amer. J. Math. 80 (1958), 632–638. MR 102806, DOI 10.2307/2372775
- R. James Milgram, The bar construction and abelian $H$-spaces, Illinois J. Math. 11 (1967), 242–250. MR 208595
- John W. Milnor and John C. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211–264. MR 174052, DOI 10.2307/1970615 61. John Morgan, Stable tangential homotopy equivalences, Ph.D. Thesis, Rice University, Houston, Tex., 1969.
- Franklin P. Peterson, A note on $H$-spaces, Bol. Soc. Mat. Mexicana (2) 4 (1959), 30–31. MR 120644
- Hans Samelson, Topology of Lie groups, Bull. Amer. Math. Soc. 58 (1952), 2–37. MR 45129, DOI 10.1090/S0002-9904-1952-09544-6
- Hans Scheerer, Homotopieäquivalente kompakte Liesche Gruppen, Topology 7 (1968), 227–232 (German). MR 229259, DOI 10.1016/0040-9383(68)90003-7
- Jean-Pierre Serre, Quelques calculs de groupes d’homotopie, C. R. Acad. Sci. Paris 236 (1953), 2475–2477 (French). MR 55684
- Larry Smith, On the type of an associative $H$-space of rank two, Tohoku Math. J. (2) 20 (1968), 511–515. MR 243523, DOI 10.2748/tmj/1178243075
- 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 66646, DOI 10.1007/BF02564267
- James Stasheff, On homotopy Abelian $H$-spaces, Proc. Cambridge Philos. Soc. 57 (1961), 734–745. MR 141123, DOI 10.1017/S0305004100035878
- James D. Stasheff, Manifolds of the homotopy type of (non-Lie) groups, Bull. Amer. Math. Soc. 75 (1969), 998–1000. MR 246319, DOI 10.1090/S0002-9904-1969-12333-5
- James Dillon Stasheff, Homotopy associativity of $H$-spaces. I, II, Trans. Amer. Math. Soc. 108 (1963), 275-292; ibid. 108 (1963), 293–312. MR 0158400, DOI 10.1090/S0002-9947-1963-0158400-5
- Masahiro Sugawara, On a condition that a space is an $H$-space, Math. J. Okayama Univ. 6 (1957), 109–129. MR 86303
- Masahiro Sugawara, A condition that a space is group-like, Math. J. Okayama Univ. 7 (1957), 123–149. MR 97066
- Masahiro Sugawara, On the homotopy-commutativity of groups and loop spaces, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math. 33 (1960/61), 257–269. MR 120645, DOI 10.1215/kjm/1250775911
- Masahiro Sugawara, Some remarks on homotopy equivalences and $H$-spaces, Math. J. Okayama Univ. 8 (1958), 125–131. MR 104224
- Emery Thomas, Steenrod squares and $H$-spaces, Ann. of Math. (2) 77 (1963), 306–317. MR 145526, DOI 10.2307/1970217
- Emery Thomas, Steenrod squares and $H$-spaces. II, Ann. of Math. (2) 81 (1965), 473–495. MR 177408, DOI 10.2307/1970399
- 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 0220276
- Hirosi Toda, Generalized Whitehead products and homotopy groups of spheres, J. Inst. Polytech. Osaka City Univ. Ser. A 3 (1952), 43–82. MR 60822
- Hirosi Toda, Composition methods in homotopy groups of spheres, Annals of Mathematics Studies, No. 49, Princeton University Press, Princeton, N.J., 1962. MR 0143217
- George W. Whitehead, Note on a theorem of Sugawara, Bol. Soc. Mat. Mexicana (2) 4 (1959), 33–41. MR 123320
- George W. Whitehead, On mappings into group-like spaces, Comment. Math. Helv. 28 (1954), 320–328. MR 65927, DOI 10.1007/BF02566938 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).
Additional Information
- 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
- MathSciNet review: 0278303