@article{SM_1991_69_1_a5,
author = {V. M. Buchstaber and A. N. Kholodov},
title = {Formal groups, functional equations, and generalized cohomology theories},
journal = {Sbornik. Mathematics},
pages = {77--97},
year = {1991},
volume = {69},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1991_69_1_a5/}
}
V. M. Buchstaber; A. N. Kholodov. Formal groups, functional equations, and generalized cohomology theories. Sbornik. Mathematics, Tome 69 (1991) no. 1, pp. 77-97. http://geodesic.mathdoc.fr/item/SM_1991_69_1_a5/
[1] Elliptic curves and modular forms in algebraic topology, Lect. Notes in Math., 1326, Springer, Berlin, 1988 | MR | Zbl
[2] Abel N. H., “Methode generale pour trouver des fonctions d'une seule quantite variable lorsqu'une propriete de ces fonctions est exprimee par une equation entre deux variables”, ØE uvres completes, Christiania, 1881, 1–10
[3] Abel N. H., “Recherche des fonctions de deux quantites variables idependantes $x$ et $y$, telles que $f(x, y)$, qui ont la propriete que $f(z, f(x, y))$ est une fonction symetrique de $z$, $x$ et $y$”, ØE uvres completes, I, Christiania, 1881, 61–65
[4] Bukhshtaber V. M., “Kharakter Chzhenya - Dolda v kobordizmakh, I”, Matem. sb., 83 (125) (1970), 575–595 | Zbl
[5] Bukhshtaber V. M., “Dvuznachnaya formalnaya gruppa. Algebraicheskaya teoriya i prilozheniya k kobordizmam”, Izv. AN SSSR. Ser. matem., 39 (1975), 1044–1064 | Zbl
[6] Bukhshtaber V. M., “Kogomologicheskie operatsii i formalnaya gruppa v kobordizmakh”, Dopolnenie k knige V. Sneit, Algebraicheskii kobordizm i $K$-teoriya, Mir, M., 1983, 227–248 | MR
[7] Golubev V. V., Lektsii po analiticheskoi teorii differentsialnykh uravnenii, M., Gostekhizdat, 1950
[8] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, IL, M., 1951
[9] Konner P., Floid E., “O sootnoshenii teorii kobordizmov i $K$-teorii”, Dopolnenie k kn. Gladkie periodicheskie otobrazheniya, Mir, M., 1968
[10] Kordzaya K. D., Nadiradze R. G., “Ellipticheskie rody $N$-go urovnya i umbralnyi analiz”, Soobsch. AN GSSR, 1989 | Zbl
[11] Krichever I. M., “Formalnye gruppy i formula Ati - Khirtserbrukha”, Izv. AN SSSR. Ser. matem., 38 (1974), 1289–1304 | Zbl
[12] Krichever I. M., “Prepyatstvie dlya suschestvovaniya $S^1$-deistviya. Bordizmy razvetvlennykh nakryvayuschikh”, Izv. AN SSSR. Ser. matem., 40 (1976), 828–844 | Zbl
[13] Landweber P. S., “Homological properties of comodules over $MU_*(MU)$ and $BP_*(BP)$”, American J. Math., 98 (1976), 573–591 | DOI | MR
[14] Landweber P. S., “Elliptic cohomology and modular forms”, Lect. Notes in Math., 1326 (1988), 55–68 | DOI | MR | Zbl
[15] Landweber P. S., “Supersingular elliptic curves and congruences for Legendre polynomials”, Lect. Notes in Math., 1326 (1988), 69–93 | DOI | MR | Zbl
[16] Lazard M., “Sur les groupes de Lie formels a un parametre”, Bull. Soc. Math. France., 83 (1955), 251–274 | MR | Zbl
[17] Mullin R., Rota G.-C., On the foundations of combinatorial theory III: Theory of binomial enumerations, Graph theory and its applications, N. Y., Academic Press, 1970 | MR
[18] Novikov S. P., “Metody algebraicheskoi topologii s tochki zreniya teorii kobordizmov”, Izv. AN SSSR. Ser. matem., 31 (1967), 855–951 | Zbl
[19] Ochanine S. D., “Sur les genres multiplicatifs definis par des integrates elliptiques”, Topology, 26 (1987), 143–151 | DOI | MR | Zbl
[20] Ochanine S. D., “Genres elliptiquees equivariants”, Lect. Notes in Math., 1326 (1988), 107–122 | DOI | MR | Zbl
[21] Painleve P., “Sur les equations differentielles du second ordre et d'ordre superieur, l'integrale generale est uniforme”, Acta Math., 25 (1902), 1–86 | DOI | MR
[22] Quillen D., “On the formal group laws of unoriented and complex cobordism theory”, Bull. Amer. Math. Soc., 75 (1969), 1293–1298 | DOI | MR | Zbl
[23] Quillen D., “Elementary proofs of some results of cobordism theory using Steenrod operations”, Adv. Math., 7 (1971), 29–56 | DOI | MR | Zbl
[24] Ray N., “Extension of umbral calculus: penumbral coalgebras and generalised Bernoulli numbers”, Adv. Math., 61 (1986), 49–100 | DOI | MR | Zbl
[25] Ray N., “Symbolic calculus: a 19th century approach to $MU$ and $BP$”, Homotopy theory, Cambridge Univ. Press, Cambridge, 1987, 195–237 | MR
[26] Roman S., The umbral calculus, Academic Press, N. Y., 1984 | MR
[27] Roman S., Rota G.-C., “The umbral calculus”, Adv. Math., 27 (1978), 95–188 | DOI | MR | Zbl
[28] Rudyak Yu. B., “Teoremy o tochnosti v teoriyakh kogomologii $MU$, $BP$, i $P(n)$”, Matem. zametki, 40:1 (1986), 115–126 | MR | Zbl
[29] Khirtserbrukh F., Topologicheskie metody v algebraicheskoi geometrii, Mir, M., 1973
[30] Hirzerbruch F., Elliptic genera of level $N$ for complex manifolds, Preprint. MPI/88-24
[31] Kholodov A. N., “Tenevoi analiz na mnogoznachnykh formalnykh gruppakh i proektory Adamsa v $K$-teorii”, Matem. sb., 137 (179) (1988), 417–431 | Zbl
[32] Witten E., “Elliptic genera and quantum field theory”, Comm. Math. Phys., 109 (1987), 526–535 | DOI | MR
[33] Witten E., “The index of the Dirac operator in loop space”, Lect. Notes in Math., 1326 (1988), 161–181 | DOI | MR | Zbl