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Formal groups, power systems and Adams operators
Sbornik. Mathematics, Tome 13 (1971) no. 1, pp. 80-116 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper provides a systematic presentation of the connection between the theory of one-dimensional formal groups and the theory of unitary cobordism. Two new algebraic concepts are introduced: formal power systems and two-valued formal groups. A presentation of the general theory of formal power systems is given, and it is shown that cobordism theory gives a nontrivial example of a system which is not a formal group. A two-valued formal group is constructed whose ring of coefficients is closely related to the bordism ring of a symplectic manifold. Finally, applications of formal groups and power systems are made to the theory of fixed points of periodic transformations of quasicomplex manifolds. Bibliography: 17 titles. 
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V. M. Buhštaber; S. P. Novikov. Formal groups, power systems and Adams operators. Sbornik. Mathematics, Tome 13 (1971) no. 1, pp. 80-116. http://geodesic.mathdoc.fr/item/SM_1971_13_1_a4/

[1] M. Atya, Lektsii po $K$-teorii, Mir, Moskva, 1967 | MR

[2] V. M. Bukhshtaber, “Kharakter Chzhenya–Dolda v teorii kobordizmov. I”, Matem. sb., 83(125) (1970), 575–595 | Zbl

[3] F. Hirzebruch, Neue topologische Methoden in der algebraischen Geometrie, Springer-Verlag, Berlin–Gottingen–Heidelberg, 1956 | MR | Zbl

[4] T. Khonda, “Formalnye gruppy i dzeta-funktsii”, Matematika, 13:6 (1969), 3–17 | MR

[5] G. G. Kasparov, “Invarianty klassicheskikh linzovykh mnogoobrazii v teorii kobordizmov”, Izv. AN SSSR, seriya matem., 33 (1969), 735–747 | MR | Zbl

[6] M. Kervaire, I. Milnor, “Bernoulli number, nomotopy groups and theorem oi Rohlin”, Proc. Internal. Congr. Math., Univ. Press, Cambridge, 1958, 454–458

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

[8] M. Lazard, “Sur les groupes de Lie formels a un parametre”, Bull. Soc. Math. France, 83 (1955), 251–274 | MR | Zbl

[9] A. S. Mischenko, “Mnogoobraziya s deistviem gruppy $Z_p$ i nepodvizhnye tochki”, Matem. zametki, 4:4 (1968), 381–386 | Zbl

[10] I. Milnor, “Cobordism ring and complex analogue”, Amer. J. Math., 82:3 (1960), 505–521 | DOI | MR | Zbl

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

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

[13] S. P. Novikov, “Operatory Adamsa i nepodvizhnye tochki”, Izv. AN SSSR, seriya matem., 32 (1968), 1245–1263 | MR

[14] D. Quillen, “On the formal group laws of unoriented and complex cobordism theory”, Bull. Amer. Math. Soc., 75:6 (1969), 1293–1298 | DOI | MR | Zbl

[15] M. Atya, R. Bott, “Zametki o teoreme Lefshetsa o nepodvizhnoi tochke”, Matematika, 10:4 (1966), 101–139

[16] P. Konner, Z. Floid, Gladkie periodicheskie otobrazheniya, Mir, Moskva, 1969

[17] A. S. Mischenko, “Bordizmy s deistviem gruppy $Z_p$ i nepodvizhnye tochki”, Matem. sb., 80(122) (1969), 307–313 | Zbl