Bulletin of the American Mathematical Society

Author(s): George W. Whitehead
Journal: Bull. Amer. Math. Soc. 8 (1983), 1-29.
MSC (1980): Primary 55-03; Secondary 01-02, 01A60, 01A65, 55M05, 55N15, 55N20, 55N22, 55N40, 55P-T, 57-03, 57R20, 57R42, 57R75, 57R77, 57R90, 57R95
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1930 Hopf, Heinz, Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche, Math. Ann. 104 (1931), 639-665.

1932 Čech, Edouard, Höherdimensionale Homotopiegruppen, Verhandlungen des Internationalen Mathematikerkongress, Zürich, 1932, p. 203; Orel Füssli, Zurich and Leipzig, 1932.

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1946 Steenrod, Norman E. Products of cocycles and extensions of mappings, Ann. of Math. (2) 48 (1947), 290-320. MR 22071

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1946-50 Leray, Jean L'anneau spectral et l'anneau filtré d'homologie d'un espace localement compact et d'une application continue, J. Math. Pures Appl. (9) 29 (1950), 1-139. MR 37505

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1950 Pontryagin, L. Homotopy classification of the mappings of an (n + 2)-dimensional sphere on an n-dimensional, Dokl. Akad. Nauk SSSR (N.S.) 70 (1950), 957-959. (Russian) MR 42121

1950 Serre, Jean-Pierre Homologie singulière des espaces fibrés, Ann. of Math. (2) 54 (1951), 425-505. MR 45386

1950 Whitehead, George W. The (n + 2)-nd homotopy of the n-sphere, Ann. of Math. (2) 52 (1950), 245-247. MR 37507

1950-52 Eilenberg, Samuel and Mac Lane, Saunders On the groups H (II, n), Ann. of Math. (2) 58 (1953), 55-106; 60 (1954), 49-139, 513-557.

1951 Postnikov, M. M. Investigations in homotopy theory of continuous mappings, Amer. Math. Soc. Transl. (2); 7 (1957) 1-134; 9 (1959), 115-153. MR 94800

1951 Steenrod, Norman E. The topology of fibre bundles, Princeton Univ. Press, Princeton, N. J., 1951. MR 39258

1951 Steenrod, Norman E. Reduced powers of cohomology classes, Ann. of Math. (2) 56 (1952), 47-67. MR 48026

1951 Whitehead, George W. On the Freudenthal theorems, Ann. of Math. (2) 57 (1953), 209-228. MR 55683

1952 Serre, Jean-Pierre Groupes d'homotopie et classes de groupes abéliens, Ann. of Math. (2) 58 (1953), 258-294. MR 59548

1952 Serre, Jean-Pierre Cohomologie modulo 2 des complexes d 'Eilenberg-Mac Lane, Comment. Math. Helv. 27 (1953), 198-232. MR 60234

1952 Toda, Hirosi Generalized Whitehead products and homotopy groups of spheres, J. Inst. Polytech Osaka City Univ. Ser. A. Math. 3 (1952), 43-82. MR 60822

1952-53 Adem, José The relations on Steenrod powers of cohomology classes, Algebraic Geometry and Topology, Sympos. in Honor of S. Lefschetz, Princeton Univ. Press, Princeton, N. J., 1957. MR 85502

1953 Cartan, Henri Algèbres d 'Eilenbrg-Mac Lane et homotopie, Séminaire Henri Cartan, Vol. 7, 1954/55; Secrétariat Mathématique, Paris, 1955.

1953 Thom, René Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17-86. MR 61823

1953 Toda, Hirosi Complex of the standard paths and n-ad homotopy groups, J. Inst. Polytech. Osaka City Univ. Ser. A. Math. 6 (1955), 101-120. MR 75589

1953-57 Spanier, E. H. and Whitehead, J. H. C. Obstructions to compression, Quart. J. Math. Oxford (2) 6 (1955), 91-100. MR 71770

1953-57 Spanier, E. H. and Whitehead, J. H. C. Duality in homotopy theory, Mathematika 2 (1955), 56-80. MR 74823

1953-57 Spanier, E. H. and Whitehead, J. H. C. The theory of carriers and S-theory, Algebraic Geometry and Topology, Sympos. in Honor of S. Lefschetz, Princeton Univ. Press, Princeton, N. J., 1957. MR 84772

1953-57 Spanier, E. H. and Whitehead, J. H. C. Duality in relative homotopy theory, Ann. of Math. (2) 67 (1958), 203-238. MR 105105

1954 Hilton, P. J. On the homotopy groups of the union of spheres, J. London Math. Soc. 30 (1955), 154-172. MR 68218

1954 James, I. M. Reduced product spaces, Ann. of Math. (2) 62 (1955), 170-197. MR 73181

1954 James, I. M. On the suspension triad, Ann. of Math. (2) 63 (1956), 191-247. MR 77922

1954 James, I. M. The suspension triad of a sphere, Ann. of Math. (2) 63 (1956), 407-429. MR 79263

1954 Whitehead, George W. Homotopy groups of joins and unions, Trans. Amer. Math. Soc. 83 (1956), 55-69. MR 80918

1955 Hurewicz, Witold, On the concept of fibre space, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 956-961. MR 73987

1955 Toda, Hirosi, Calcul de groupes d'homotopie des sphères, C. R. Acad. Sci. Paris 240 (1955), 147-149. MR 68215

1956 Brown, Edgar H., Jr. Finite computability of Postnikov complexes, Ann. of Math. (2) 65 (1957), 1-20. MR 83733

1956 Kudo, Tatsuji and Araki, Shoro Topology of H, Mem. Fac. Sci. Kyushu Univ. Ser. A 10 (1956), 85-120. MR 87948

1957 Adams, J. F. On the structure and applications of the Steenrod algebra, Comment. Math. Helv. 32 (1958), 180-214. MR 96219

1957 Bott, Raoul The stable homotopy of the classical groups, Ann. of Math. (2) 70 ( 1959), 313-337. MR 110104

1957 Milnor, John W. The Steenrod algebra and its dual, Ann. of Math. (2) 67 ( 1958), 150-171. MR 99653

1958 Adams, J. F. On the non-existence of elements of Hopf invariant one, Ann. of Math. (2) 72 (1960), 20-104. MR 141119

1958 Hirsch, Morris W. Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959), 242-276. MR 119214

1958 Lima, E. L. The Spanier-Whitehead duality in new homotopy categories, Summa Brasil. Math. 4 (1959), 91-148. MR 116332

1958 Markov, A. The insolubility of the problem of homeomorphy, Dokl. Akad. Nauk USSR 121 (1958), 218-220. (Russian) MR 97793

1958 Massey, W. S. On the Stiefel-Whitney classes of a manifold, Amer. J. Math. 82 (1960), 92-102. MR 111053

1958 Milnor, John W. On the cobordism ring Ω* and a complex analogue. I, Amer. J. Math. 82 (1960), 505-521. MR 119209

1958 Toda, Hirosi p-primary components of homotopy groups, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math. 31 (1958), 129-142, 143-160, 191-210.

1958 Whittlesey, E. F. Finite surfaces: a study of finite 2-complexes, Math. Mag. 34 (1960/61), 11-22, 67-80.

1959 Atiyah, M. F. and Hirzebruch, F. E. P. Vector bundles and homogeneous spaces, Proc. Sympos. Pure Math., vol. 3, Amer. Math. Soc. Providence, R. I., 1961, pp. 7-38. MR 139181

1959 Browder, William Homology operations and loop spaces, Illinois J. Math. 4 (1960), 347-357. MR 120646

1959 Brown, Edgar H., Jr. Cohomology theories, Ann. of Math. (2) 75 (1962), 467-484; 78 (1963), 201. MR 138104

1959 Wall, C. T. C. Determination of the cobordism ring, Ann. of Math. (2) 72 (1960), 292-311. MR 120654

1959 Whitehead, George W. Generalized homology theories, Trans. Amer. Math. Soc. 102 (1962), 227-283. MR 137117

1960 Atiyah, M. F. Bordism and cobordism, Proc. Cambridge Philos. Soc. 57 (1961), 200-208. MR 126856

1961 Dyer, Eldon and Lashof, R. K. Homology of iterated loop spaces, Amer. J. Math. 84 (1962), 35-88. MR 141112

1962 Brown, Edgar H., Jr. and Peterson, Franklin P. Relations among characteristic classes. I, Topology 3 Supp. 1 (1964), 39-52. MR 163326

1962 Toda, Hirosi Composition methods in homotopy groups of spheres, Princeton Univ. Press, Princeton, N. J., 1962. MR 143217

1963 Mimura, Mamoru and Toda, Hirosi The (n + 20)-th homotopy groups of n-spheres, J. Math. Kyoto Univ. 1 (1963), 37-58. MR 157384

1964 Freyd, Peter Stable homotopy, Proc. Conf. Categorical Algebra (LaJolla, 1965), Springer-Verlag, Berlin-Heidelberg-New York, 1966, pp. 121-172. MR 211399

1964 Mimura, Mamoru, On the genralized Hopf homomorphism and the higher composition, J. Math. Kyoto Univ. 4 (1964/65), 171-190, 301-326. MR 179793

1965 Brown, Edgar H., Jr. and Peterson, Franklin P. A spectrum whose Z, Topology 5 (1966), 149-154. MR 192494

1965 Milgram, R. James Iterated loop spaces, Ann. of Math. (2) 84 (1966), 386-403. MR 206951

1965 Anderson, Donald W., Brown, Edgar H., Jr. and Peterson, Franklin P. The structure of the Spin cobordism ring, Ann. of Math. (2) 86 ( 1967), 271-298. MR 219077

1966 Bousfield, A. K. et al. The mod p lower central series and the Adams spectral sequence, Topology 5 (1966), 331-342. MR 199862

1966 Massey, W. S. and Peterson, Franklin P. The mod 2 cohomology structure of certain fibre spaces. II, Mem. Amer. Math. Soc. No. 74 (1967). MR 226637

1967 Novikov, S. P. Methods of algebraic topology from the point of view of cobordism theory, Izv. Akad. Nauk SSSR Ser. Math. 31 (1967), 855-951. (Russian) MR 221509

1968 Boardman, J. M. and Vogt, R. M. Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Math., vol. 347, Springer-Verlag, Berlin and New York, 1973. MR 420609

1969 Quillen, Daniel On the formal group laws of unoriented and complex cobordism theory, Bull. Amer. Math. Soc. 75 (1969), 1293-1298. MR 253350

1969-70 Smith, Larry On realizing complex bordism modules. Applications to the stable homotopy of spheres, Amer. J. Math. 92 (1970), 793-856; 93 (1971), 226-263. MR 275429

1970 May, J. Peter The geometry of iterated loop spaces, Lecture Notes in Math., vol. 271, Springer-Verlag, Berlin and New York, 1972. MR 420610

1970 Toda, Hirosi On spectra realizing parts of the Steenrod algebra, Topology 10 (1971), 53-65. MR 271933

1970 Sullivan, Dennis Geometric topology. Part I, Massachusetts Institute of Technology, Cambridge, Mass., 1971. MR 494074

1971 Brown, Edgar H., Jr. and Gitler, Samuel A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra, Topology 12 (1973), 283-295. MR 391071

1971 Kahn, Daniel S. and Priddy, Stewart B. Applications of the transfer to stable homotopy theory, Bull. Amer. Math. Soc. 78 ( 1972), 981-997. MR 309109

1972 Oda, Shichiro The stable homotopy groups of spheres. II, Hiroshima Math. J. 2 (1972), 99-161. MR 322865

1972 Snaith, V. P. A stable decomposition of ΩⁿSⁿX, J. London Math. Soc. (2) 7 (1974), 577-583. MR 339155

1973 Segal, Graeme Configuration spaces and iterated loop spaces, Invent. Math. 21 (1973), 213-222. MR 331377

1973 Thomas, P. E. and Zahler, Raphael Non-triviality of the stable homotopy element γ, J. Pure Appl. Algebra 4 (1974), 189-203. MR 356049

1974 Mimura, Mamoru, Mori, Masamitsu and Oda, Nobuyuki Determination of 2-components of the 23 and 24-stems in homotopy groups of spheres, Mem. Fac. Sci. Kyushu Univ. Ser. A 29 (1975), 1-42. MR 375300

1974 Oka, Shichiro and Toda, Hirosi Non-triviality of an element in the stable homotopy groups of spheres, Hiroshima Math. J. 5 (1975), 115-125. MR 380792

1976 Brown, Edgar H., Jr. and Peterson, Franklin P. On immersions of n-manifolds, Adv. in Math. 24 (1977), 74-77. MR 436169

1976 Mahowald, Mark A new infinite family in , Topology 16 (1977), 249-256.

1976 Miller, Haynes, Ravenel, Douglas C. and Wilson, W. Stephen Periodic phenomena in the Adams-Novikov spectral sequence, Ann. of Math. (2) 106 (1977), 469-516. MR 458423

1977 Oda, Nobuyuki, On the 2-components of the unstable homotopy groups of spheres, Proc. Japan Acad. Ser. A 53 (1977), 202-205, 215-218. MR 464231

1978 Brown, Edgar H., Jr. and Peterson, Franklin P. A universal space for normal bundles of manifolds, Comment. Math. Helv. 54 (1979).

1978 Knapp, K. On the bi-stable J-homomorphism, Algebraic Topology (Aarhus, 1978), Lecture Notes in Math., vol. 763, Springer-Verlag, Berlin-Heidelberg-New York, 1979. MR 561211

1981 Cohen, Ralph L. Immersions of manifolds, Proc. Nat. Acad. Sci. U.S.A. 79 (1982), 3390-3392. MR 657550

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