Geodesic
Modules of differentials of the Atiyah–Hirzebruch spectral sequence. II
Sbornik. Mathematics, Tome 12 (1970) no. 1, pp. 59-75 Cet article a éte moissonné depuis la source Math-Net.Ru

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The subject of the article is the Atiyah–Hirzebruch spectral-sequence method in $K$-theory. In particular, one of the results is the definitive solution (in terms of homology groups) of the problem of realizing the cycles of a manifold by submanifolds, and a formula is given that connects the higher differentials of the spectral sequence with the Steenrod powers. Bibliography: 21 titles. 
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     title = {Modules of differentials of the {Atiyah{\textendash}Hirzebruch} spectral {sequence.~II}},
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V. M. Buchstaber. Modules of differentials of the Atiyah–Hirzebruch spectral sequence. II. Sbornik. Mathematics, Tome 12 (1970) no. 1, pp. 59-75. http://geodesic.mathdoc.fr/item/SM_1970_12_1_a3/

[1] Dzh. F. Adams, “O nesuschestvovanii otobrazhenii s invariantom Khopfa, ravnym edinitse”, Matematika, 5:4 (1961), 3–86

[2] J. F. Adams, “On Chern characters and structure of the unitary group”, Proc. Camb. Phil. Soc., 57 (1961), 189–199 | DOI | MR | Zbl

[3] Dzh. F. Adams, “Vektornye polya na sferakh”, Matematika, 7:6 (1963), 49–79

[4] Dzh. F. Adams, “O gruppakh $J(X)$”, Matematika, 12:3 (1968), 37–97

[5] J. F. Adams, M. F. Atiyah, “$K$-theory and the Hopf invariant”, Quart. J. Math., 17 (1966), 31–38 | DOI | MR | Zbl

[6] J. Adem, “The iteration of the Steenrod squares in Algebraic Topology”, Proc. Nat. Acad. Sci. USA, 38 (1952), 720–726 | DOI | MR | Zbl

[7] J. Adem, “Relation on iterated reduced powers”, Proc. Nat. Acad. Sci. USA, 39 (1953), 636–638 | DOI | MR | Zbl

[8] M. F. Atiyah, F. Hirzebruch, “Analytic cycles on complex manifold”, Topology, 1 (1961), 25–45 | DOI | MR

[9] M. Atya, “Prostranstva Toma”, Matematika, 10:5 (1966), 48–69

[10] M. F. Atiyah, “Power operations in $K$-theory”, Quart. J. Math., 17 (1966), 165–193 | DOI | MR | Zbl

[11] S. Araki, H. Toda, “Multiplicative structures in $\mod q$ cohomology theory. I”, Osaka J. Math., 2:1 (1965), 71–115 ; “II”, Osaka J. Math., 3:1 (1966), 81–120 | MR | Zbl | MR | Zbl

[12] V. M. Bukhshtaber, “Moduli differentsialov spektralnoi posledovatelnosti Atya–Khirtsebrukha”, Matem. sb., 78(120) (1969), 307–320 | Zbl

[13] H. Cartan, “Sur les groupes d'Eilenberg–Maclane. I, II”, Proc. Nat. Acad. Sci. USA, 40 (1954), 467–471, 704–707 | DOI | MR | Zbl

[14] E. Dyer, “Chern characters of certain complexes”, Math. Z., 80 (1963), 363–373 | DOI | MR | Zbl

[15] P. Konner, E. Floid, “O sootnoshenii teorii bordizmov i $K$-teorii”, Dopolnenie k kn.: Gladkie periodicheskie otobrazheniya, Mir, Moskva, 1969

[16] A. S. Mischenko, “Spektralnye posledovatelnosti tipa Adamsa”, Matem. zametki, 1:3 (1967), 339–346 | Zbl

[17] S. P. Novikov, “Gomotopicheskie svoistva kompleksov Toma”, Matem. sb., 57(99) (1962), 406–442

[18] S. P. Novikov, “Metody algebraicheskoi topologii s tochki zreniya teorii kobordizmov”, Izv. AN SSSR, seriya matem., 31 (1967), 855–951 | Zbl

[19] Zh.-P. Serr, “Gomotopicheskie gruppy i klassy abelevykh grupp”, Rassloennye prostranstva, IL, Moskva, 1958

[20] M. Spivak, “Spaces satisfying Poincare duality”, Topology, 6:1 (1967), 77–101 | DOI | MR | Zbl

[21] P. Tom, “Nekotorye svoistva “v tselom” differentsiruemykh mnogoobrazii”, Rassloennye prostranstva, IL, Moskva, 1958