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Complex cobordism and formal groups
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 67 (2012) no. 5, pp. 891-950 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper surveys the current state of the theory of cobordism, focusing on geometric and universal properties of complex cobordism, the Landweber–Novikov algebra, and the formal group law of geometric cobordisms. The relationships with $K$-theory, algebraic cycles, formal group laws, compact Lie group actions on manifolds, toric topology, infinite-dimensional Lie algebras, and nilmanifolds are described. The survey contains key results and open problems. Bibliography: 124 titles.
Keywords: Landweber–Novikov algebra, Adams operations, Chern–Dold character
Mots-clés : Atiyah–Hirzebruch spectral sequence, Hirzebruch genera. 
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V. M. Buchstaber. Complex cobordism and formal groups. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 67 (2012) no. 5, pp. 891-950. http://geodesic.mathdoc.fr/item/RM_2012_67_5_a1/

[1] V. M. Bukhshtaber, A. S. Mishchenko, S. P. Novikov, “Formal groups and their role in the apparatus of algebraic topology”, Russian Math. Surveys, 26:2 (1971), 63–90 | DOI | MR | Zbl | Zbl

[2] S. P. Novikov, “Topology in the 20th century: a view from the inside”, Russian Math. Surveys, 59:5 (2004), 803–829 | DOI | DOI | MR | Zbl

[3] S. P. Novikov, Predislovie k kn.: Kobordizmy v Sovetskom Soyuze 1967–1979, Topologicheskaya biblioteka, 4, eds. S. P. Novikov, I. A. Taimanov, M.–Izhevsk, Institut kompyuternykh issledovanii, 2011, 9–13

[4] Kobordizmy v Sovetskom Soyuze 1967–1979, Topologicheskaya biblioteka, 4, eds. S. P. Novikov, I. A. Taimanov, M.–Izhevsk, Institut kompyuternykh issledovanii, 2011, 584 pp.

[5] S. P. Novikov, Topology, Encyclopaedia Math. Sci., 12, Springer, Berlin, 1996, 319 pp. | MR | MR | Zbl

[6] H. Poincaré, “Analysis situs”, J. Ecole Polytech. (2), 1 (1895), 1–121 ; Рђ. ПуанкарРμ, “Analysis situs”, Р�збранныРμ труды, С‚. II, Наука, Рњ., 1972, 457–807 | Zbl | MR | Zbl

[7] M. F. Atiyah, “Bordism and cobordism”, Proc. Cambridge Philos. Soc., 57:2 (1961), 200–208 | DOI | MR | Zbl

[8] R. Thom, “Quelques propriétés globales de variétés différentiables”, Comm. Math. Helv., 28 (1954), 17–86 | DOI | MR | Zbl

[9] J. Milnor, “On the cobordism ring $\Omega_*$ and a complex analogue. Part I”, Amer. J. Math., 82:3 (1960), 505–521 | DOI | MR | Zbl

[10] S. P. Novikov, “Some problems in the topology of manifolds connected with the theory of Thom spaces”, Soviet Math. Dokl., 1 (1960), 717–720 | MR | Zbl

[11] S. P. Novikov, “Gomotopicheskie svoistva kompleksov Toma”, Matem. sb., 57(99):4 (1962), 407–442 | MR | Zbl

[12] S. P. Novikov, “The methods of algebraic topology from the viewpoint of cobordism theory”, Math. USSR-Izv., 1:4 (1967), 827–913 | DOI | MR | Zbl | Zbl

[13] T. Katsura, Yu. Shimizu, K. Ueno, “Complex cobordism ring and conformal field theory over $\mathbb{Z}$”, Math. Ann., 291:3 (1991), 551–571 | DOI | MR | Zbl

[14] T. Coates, A. Givental, “Quantum cobordisms and formal group laws”, The unity of mathematics, Progr. Math., 244, Birkhäuser Boston, Boston, MA, 2006, 155–171 | DOI | MR | Zbl

[15] M. Levine, F. Morel, Algebraic cobordism, Springer Monogr. Math., Springer, Berlin, 2007, xii+244 pp. | DOI | MR | Zbl

[16] S. P. Novikov, “Various doublings of Hopf algebras. Operator algebras on quantum groups, complex cobordisms”, Russ. Math. Surveys, 47:5 (1992), 198–199 | DOI | MR | Zbl

[17] V. M. Buchstaber, “Semigroups of maps into groups, operator doubles, and complex cobordisms”, Topics in topology and mathematical physics, Amer. Math. Soc. Transl. Ser. 2, 170, Amer. Math. Soc., Providence, RI, 1995, 9–31 | MR | Zbl

[18] V. G. Drinfel'd, “Hopf algebras and the quantum Yang–Baxter equation”, Soviet Math. Dokl., 32 (1985), 256–258 | MR | Zbl

[19] C. Kassel, Quantum groups, Grad. Texts in Math., 155, Springer-Verlag, New York, 1995, xii+531 pp. | MR | Zbl

[20] M. A. Semenov-Tyan-Shanskii, “Poisson–Lie groups. The quantum duality principle and the twisted quantum double”, Theoret. and Math. Phys., 93:2 (1992), 1292–1307 | DOI | MR | Zbl

[21] M. Demazure, “Motifs des variétés algébriques”, Séminaire N. Bourbaki, 1969/70, Exp. No 365, 1971, 19–38 | Zbl

[22] P. S. Landweber, “Cobordism operations and Hopf algebras”, Trans. Amer. Math. Soc., 129 (1967), 94–110 | DOI | MR | Zbl

[23] S. P. Novikov, “Adams operators and fixed points”, Math. USSR-Izv., 2:6 (1968), 1193–1211 | DOI | MR | Zbl | Zbl

[24] V. M. Buhštaber, “Modules of differentials of the Atiyah–Hirzebruch spectral sequence. II”, Math. USSR-Sb., 12:1 (1970), 59–75 | DOI | MR | Zbl

[25] A. V. Shokurov, “Relations between the Chern numbers of quasicomplex manifolds”, Math. Notes, 26:1 (1979), 560–566 | DOI | MR | Zbl

[26] D. C. Ravenel, Complex cobordism and stable homotopy groups of spheres, 2nd ed., AMS Chelsea Publishing, Providence, RI, 2004, xix+395 pp. | MR | Zbl

[27] H. Miller, Kervaire invariant one [after M. A. Hill, M. J. Hopkins, and D. C. Ravenel], Séminaire N. Bourbaki, 2010/2011, Exp. No 1029, 63ème année, 2011, 30 pp.

[28] R. Stong, Notes on cobordism theory, Math. Notes, Univ. of Tokyo Press, Tokyo, 1968, v+354+lvi pp. | MR | MR | Zbl | Zbl

[29] F. Hirzebruch, “A Riemann–Roch theorem for differentiable manifolds”, Séminaire N. Bourbaki, 1958/59, 1959, 129–149 | MR | Zbl

[30] M. F. Atiyah, F. Hirzebruch, “Riemann–Roch theorems for differentiable manifolds”, Bull. Amer. Math. Soc., 65 (1959), 276–281 | DOI | MR | Zbl

[31] E. Dyer, “Relations between cohomology theories”, Colloquium on Algebraic Topology (Aarhus, 1962), Aarhus University, Aarhus, Denmark, 1962, 89–93 | Zbl

[32] I. Panin, “Oriented cohomology theories of algebraic varieties”, $K$-Theory, 30:3 (2003), 265–314 | DOI | MR | Zbl

[33] I. Panin, A. Smirnov, “Riemann–Roch theorems for oriented cohomology”, Axiomatic, enriched and motivic homotopy theory, NATO Sci. Ser. II Math. Phys. Chem., 131, Kluwer Acad. Publ., Dordrecht, 2004, 261–333 | DOI | MR | Zbl

[34] I. Panin, “Oriented cohomology theories of algebraic varieties. II. (After I. Panin and A. Smirnov.)”, Homology, Homotopy Appl., 11:1 (2009), 349–405 | MR | Zbl

[35] D. Quillen, “Elementary proofs of some results of cobordism theory using Steenrod operations”, Adv. in Math., 7 (1971), 29–56 | DOI | MR | Zbl

[36] V. Buchstaber, N. Ray, “Operations and quantum doubles in complex oriented cohomology theory”, Homology, Homotopy Appl., 1 (1999), 169–185 (electronic) | MR | Zbl

[37] V. M. Buhštaber, S. P. Novikov, “Formal groups, power systems and Adams operators”, Math. USSR-Sb., 13:1 (1971), 80–116 | DOI | MR | Zbl | Zbl

[38] V. M. Buhštaber, “The Chern–Dold character in cobordisms. I”, Math. USSR-Sb., 12:4 (1970), 573–594 | DOI | MR | Zbl | Zbl

[39] S. Ochanine, “Sur les genres multiplicatifs définis par des intégrales elliptiques”, Topology, 26:2 (1987), 143–151 | DOI | MR | Zbl

[40] F. Hirzebruch, T. Berger, R. Jung, Manifolds and modular forms, Aspects Math., E20, Friedr. Vieweg Sohn, Braunschweig, 1992, xii+211 pp. | MR | Zbl

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

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

[43] E. Friedlander, “An introduction to $K$-theory”, Some recent developments in algebraic $K$-theory, ICTP Lect. Notes, 23, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2008, 1–77 | MR | Zbl

[44] A. Dold, “Relations between ordinary and extraordinary homology”, Colloquium on Algebraic Topology (Aarhus, 1962), Aarhus University, Aarhus, Denmark, 1962, 2–9 | Zbl

[45] I. M. Kric̆ever, “Formal groups and the Atiyah–Hirzebruch formula”, Math. USSR-Izv., 8:6 (1974), 1271–1285 | DOI | MR | Zbl

[46] I. M. Krichever, “Generalized elliptic genera and Baker–Akhiezer functions”, Math. Notes, 47:2 (1990), 132–142 | DOI | MR | Zbl | Zbl

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

[48] J. F. Adams, “On the groups $J(X)$. IV”, Topology, 5 (1966), 21–71 | DOI | MR | Zbl

[49] I. M. James, “Reduced product spaces”, Ann. of Math. (2), 62 (1955), 170–197 | DOI | MR | Zbl

[50] T. Coates, A. Givental, “Quantum Riemann–Roch, Lefschetz and Serre”, Ann. of Math. (2), 165:1 (2007), 15–53 | DOI | MR | Zbl

[51] V. M. Buhštaber, “Modules of differentials of the Atiyah–Hirzebruch spectral sequence”, Math. USSR-Sb., 7:2 (1969), 299–313 | DOI | MR | Zbl

[52] M. F. Atiyah, F. Hirzebruch, “Analytic cycles on complex manifolds”, Topology, 1:1 (1962), 25–45 | DOI | MR | Zbl

[53] B. Totaro, “Torsion algebraic cycles and complex cobordism”, J. Amer. Math. Soc., 10:2 (1997), 467–493 | DOI | MR | Zbl

[54] B. I. Botvinnik, V. M. Buchstaber, S. P. Novikov, S. A. Yuzvinskii, “Algebraic aspects of the theory of multiplications in complex cobordism theory”, Russian Math. Surveys, 55:4 (2000), 613–633 | DOI | DOI | MR | Zbl

[55] E. H. Brown, F. P. Peterson, “A spectrum whose $Z_{p}$ cohomology is the algebra of reduced $p^\mathrm{th}$ powers”, Topology, 5 (1966), 149–154 | DOI | MR | Zbl

[56] V. M. Bukhshtaber, “Proektory v unitarnykh kobordizmakh, svyazannye s SU-teoriei”, UMN, 27:6(168) (1972), 231–232 | MR | Zbl

[57] V. M. Bukhshtaber, “Dvuznachnye formalnye gruppy. Nekotorye prilozheniya k kobordizmam”, UMN, 26:3(159) (1971), 195–196 | MR | Zbl

[58] V. M. Bukhshtaber, “Characteristic cobordism classes and topological applications of the theories of one-valued and two-valued formal groups”, J. Soviet Math., 11:6 (1979), 815–921 | DOI | MR | Zbl | Zbl

[59] V. L. Ginzburg, V. Guillemin, Y. Karshon, Moment maps, cobordisms, and Hamiltonian group actions, Math. Surveys Monogr., 98, Amer. Math. Soc., Providence, RI, 2002, viii+350 pp. | MR | Zbl

[60] V. V. Vershinin, “The ring of symplectic cobordisms”, Proc. Steklov Inst. Math., 154 (1985), 53–56 | MR | Zbl | Zbl

[61] V. M. Buchstaber, A. N. Kholodov, “Topological constructions connected with many-valued formal groups”, Math. USSR-Izv., 20:1 (1983), 1–25 | DOI | MR | Zbl | Zbl

[62] V. M. Buchstaber, “$n$-valued groups: theory and applications”, Mosc. Math. J., 6:1 (2006), 57–84 | MR | Zbl

[63] V. M. Bukhshtaber, A. V. Shokurov, “The Landweber–Novikov algebra and formal vector fields on the line”, Funct. Anal. Appl., 12:3 (1978), 159–168 | DOI | MR | Zbl

[64] P. E. Conner, E. E. Floyd, Differentiable periodic maps, Ergeb. Math. Grenzgeb., 33, Academic Press, New York; Springer-Verlag, Berlin–Goẗtingen–Heidelberg, 1964, vii+148 pp. | MR | Zbl | Zbl

[65] A. S. Mishchenko, “Manifolds with the action of the group $Z_p$ and fixed points”, Math. Notes, 4:4 (1968), 721–724 | DOI | MR | Zbl | Zbl

[66] A. S. Mishchenko, “Bordisms with the action of the group $Z_p$ and fixed points”, Math. USSR-Sb., 9:3 (1969), 291–296 | DOI | MR | Zbl

[67] G. G. Kasparov, “Invariants of classical lens manifolds in cobordism theory”, Math. USSR-Izv., 3:4 (1969), 695–705 | DOI | MR | Zbl | Zbl

[68] I. M. Krichever, “Actions of finite cyclic groups on quasicomplex manifolds”, Math. USSR-Sb., 19:2 (1973), 305–319 | DOI | MR | Zbl | Zbl

[69] S. M. Gusein-Zade, I. M. Krichever, “O formulakh dlya nepodvizhnykh tochek deistviya gruppy $Z_p$”, UMN, 28:1(169) (1973), 237–238 | MR | Zbl

[70] I. M. Krichever, “Remark on the paper ‘Actions of finite cyclic groups on quasicomplex manifolds’ ”, Math. USSR-Sb., 24:1 (1974), 145–146 | DOI | MR | Zbl

[71] S. M. Gusein-Zade, “Nepodvizhnye tochki $U$-deistvii okruzhnosti”, UMN, 26:4(160) (1971), 250 | MR | Zbl

[72] S. M. Gusein-Zade, “On the action of a circle on manifolds”, Math. Notes, 10:5 (1971), 731–734 | DOI | MR | Zbl | Zbl

[73] S. M. Gusein-Zade, “$U$-actions of a circle and fixed points”, Math. USSR-Izv., 5:5 (1971), 1127–1143 | DOI | MR | Zbl | Zbl

[74] I. M. Krichever, “Ekvivariantnye rody Khirtsebrukha. Formula Atya–Khirtsebrukha”, UMN, 30:1(181) (1975), 243–244 | MR | Zbl

[75] T. E. Panov, “Calculation of Hirzebruch genera for manifolds acted on by the group $\mathbf Z/p$ via invariants of the action”, Izv. Math., 62:3 (1998), 515–548 | DOI | DOI | MR | Zbl

[76] F. Hirzebruch, Neue topologische Methoden in der algebraischen Geometrie, Ergeb. Math. Grenzgeb., 9, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1956, viii+165 pp. | MR | Zbl | Zbl

[77] V. M. Buchstaber, N. Ray, “Universal equivariant genus and Krichever's formula”, Russian Math. Surveys, 62:1 (2007), 178–180 | DOI | DOI | MR | Zbl

[78] T. E. Panov, “Combinatorial formulae for the $\chi_y$-genus of a multioriented quasitoric manifold”, Russian Math. Surveys, 54:5 (1999), 1037–1039 | DOI | DOI | MR | Zbl

[79] T. E. Panov, “Hirzebruch genera of manifolds with torus action”, Izv. Math., 65:3 (2001), 543–556 | DOI | DOI | MR | Zbl

[80] V. M. Bukhshtaber, T. E. Panov, Toricheskie deistviya v topologii i kombinatorike, MTsNMO, M., 2004, 272 pp. | MR | Zbl

[81] E. Thomas, “Complex structures on real vector bundles”, Amer. J. Math., 89 (1967), 887–908 | DOI | MR | Zbl

[82] V. M. Buchstaber, T. E. Panov, N. Ray, “Toric genera”, Int. Math. Res. Not., 16 (2010), 3207–3262 | DOI | MR | Zbl

[83] M. W. Davis, T. Januszkiewicz, “Convex polytopes, Coxeter orbifolds and torus actions”, Duke Math. J., 62:2 (1991), 417–451 | DOI | MR | Zbl

[84] V. V. Batyrev, “Quantum cohomology rings of toric manifolds”, Journées de géométrie algébrique d'Orsay (Orsay, 1992), Astérisque, 218, 1993, 9–34 | MR | Zbl

[85] V. M. Buchstaber, N. Ray, “Toric manifolds and complex cobordisms”, Russian Math. Surveys, 53:2 (1998), 371–373 | DOI | DOI | MR | Zbl

[86] V. M. Buchstaber, T. E. Panov, N. Ray, “Spaces of polytopes and cobordism of quasitoric manifolds”, Mosc. Math. J., 7:2 (2007), 219–242 | MR | Zbl

[87] A. A. Kustarev, “Equivariant almost complex structures on quasi-toric manifolds”, Russian Math. Surveys, 64:1 (2009), 156–158 | DOI | DOI | MR | Zbl

[88] V. M. Buchstaber, S. Terzic, “Equivariant complex structures on homogeneous spaces and their cobordism classes”, Geometry, topology, and mathematical physics, S. P. Novikov's seminar: 2006–2007, Amer. Math. Soc. Transl. Ser. 2, 224, eds. V. M. Buchstaber, I. M. Krichever, Amer. Math. Soc., Providence, RI, 2008, 27–57 | MR | Zbl

[89] T. Honda, “Formal groups and zeta-functions”, Osaka J. Math., 5 (1968), 199–213 | MR | Zbl

[90] M. Atiyah, F. Hirzebruch, “Spin-manifolds and group actions”, Essays on topology and related topics, Mémoires dédiés à Georges de Rham, Springer, New York, 1970, 18–28 | MR | Zbl

[91] B. Totaro, “Chern numbers for singular varieties and elliptic homology”, Ann. of Math. (2), 151:2 (2000), 757–791 | DOI | MR | Zbl

[92] H. W. Braden, K. E. Feldman, “Functional equations and the generalised elliptic genus”, J. Nonlinear Math. Phys., 12, Suppl. 1 (2005), 74–85 | DOI | MR

[93] V. M. Buchstaber, E. Yu. Bun'kova, “Krichever formal groups”, Funct. Anal. Appl., 45:2 (2011), 99–116 | DOI | DOI | MR

[94] J. T. Tate, “The arithmetic of elliptic curves”, Invent. Math., 23:3-4 (1974), 179–206 | DOI | MR | Zbl

[95] E. T. Whittaker, G. N. Watson, A course of modern analysis, Reprint of the fourth (1927) edition. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions, Cambridge Math. Lib., Cambridge Univ. Press, Cambridge, 1996, vi+608 pp. | MR | Zbl

[96] F. Hirzebruch, “Komplexe Mannigfaltigkeiten”, Proc. Internat. Congress Math. 1958, Cambridge Univ. Press, New York, 1960, 119–136 | MR | Zbl

[97] R. E. Stong, “Relations among characteristic numbers. I”, Topology, 4:3 (1965), 267–281 ; “Relations among characteristic numbers. II”, Topology, 5:2 (1966), 133–148 | DOI | MR | Zbl | DOI | MR | Zbl

[98] A. Hattori, “Integral characteristic numbers for weakly almost complex manifolds”, Topology, 5:3 (1966), 259–280 | DOI | MR | Zbl

[99] S. D. Oshanin, “The signature of SU-varieties”, Math. Notes, 13:1 (1973), 57–60 | DOI | MR | Zbl | Zbl

[100] V. M. Buchstaber, A. P. Veselov, “Dunkl operators, functional equations, and transformations of elliptic genera”, Russian Math. Surveys, 49:2 (1994), 145–147 | DOI | MR | Zbl

[101] V. M. Buchstaber, A. P. Veselov, “On a remarkable functional equation in the theory of generalized Dunkl operators and transformations of elliptic genera”, Math. Z., 223:4 (1996), 595–607 | DOI | MR | Zbl

[102] K. E. Feldman, “Chern numbers of Chern submanifolds”, Q. J. Math., 53:4 (2002), 421–429 | DOI | MR | Zbl

[103] K. E. Feldman, “Miraculous cancellation and Pick's theorem”, Toric topology, Contemp. Math., 460, Amer. Math. Soc., Providence, RI, 2008, 71–86 | MR | Zbl

[104] L. Alvarez-Gaumé, E. Witten, “Gravitational anomalies”, Nucl. Phys. B, 234:2 (1984), 269–330 | DOI | MR

[105] G. Pick, “Geometrisches zur Zahlenlehre”, Sitzenber. Lotos Prag. (2), 19 (1900), 311–319 | Zbl

[106] V. M. Bukhshtaber, “Groups of polynomial transformations of a line, non-formal symplectic manifolds, and the Landweber–Novikov algebra”, Russian Math. Surveys, 54:4 (1999), 837–838 | DOI | DOI | MR | Zbl

[107] I. K. Babenko, I. A. Taimanov, “On nonformal simply connected symplectic manifolds”, Siberian Math. J., 41:2 (2000), 204–217 | DOI | MR | Zbl

[108] F. E. A. Johnson, E. G. Rees, “The fundamental groups of algebraic varieties”, Algebraic topology Poznań 1989, Lecture Notes in Math., 1474, Springer, Berlin, 1991, 75–82 | DOI | MR | Zbl

[109] I. K. Babenko, S. A. Bogatyi, “The amenability of the substitution group of formal power series”, Izv. Math., 75:2 (2011), 239–252 | DOI | DOI | MR | Zbl

[110] I. K. Babenko, S. A. Bogatyi, “On the group of substitutions of formal power series with integer coefficients”, Izv. Math., 72:2 (2008), 241–264 | DOI | DOI | MR | Zbl

[111] Russian Math. Surveys, 68:1 (2013), 1–68 | DOI | DOI | MR | Zbl

[112] I. M. Gel'fand, “The cohomology of infinite dimensional Lie algebra: some questions of integral geometry”, Actes du Congrès International des Mathématiciens (Nice, 1970), v. 1, Gauthier-Villars, Paris, 1971, 95–111 | MR | Zbl

[113] L. V. Goncharova, “The cohomologies of Lie algebras of formal vector fields on the line”, Funct. Anal. Appl., 7:2 (1973), 91–97 | DOI | MR | Zbl

[114] L. V. Goncharova, “The cohomologies of Lie algebras of formal vector fields on the line”, Funct. Anal. Appl., 7:3 (1973), 194–203 | DOI | MR

[115] D. B. Fuks, Cohomology of infinite-dimensional Lie algebras, Consultants Bureau, New York, 1986, xii+339 pp. | MR | MR | Zbl

[116] A. I. Malcev, “On a class of homogeneous spaces”, Amer. Math. Soc. Transl., 1951, 1951, 33 pp. | MR | MR | Zbl

[117] L. Auslander, L. Green, F. Hahn, “Flows on homogeneous spaces”, Ann. of Math. Stud., 53, Princeton Univ. Press, Princeton, NJ, 1963, vii+107 pp. | MR | MR | Zbl

[118] V. P. Snaith, “Algebraic cobordism and $K$-theory”, Mem. Amer. Math. Soc., 21:221 (1979), vii+152 pp. | MR | MR | Zbl

[119] D. Gepner, V. Snaith, “On the motivic spectra representing algebraic cobordism and algebraic $K$-theory”, Doc. Math., 14 (2009), 359–396 | MR | Zbl

[120] P. E. Conner, E. E. Floyd, The relation of cobordism to $K$-theories, Lecture Notes in Math., 28, Springer-Verlag, Berlin–New York, 1966, v+112 pp. | MR | Zbl

[121] V. Voevodsky, The Milnor conjecture, 1996 http://www.math.uiuc.edu/K-theory/0170

[122] M. Levine, R. Pandharipande, “Algebraic cobordism revisited”, Invent. Math., 176:1 (2009), 63–130 | DOI | MR | Zbl

[123] I. Panin, K. Pimenov, O. Roendigs, A universality theorem for Voevodsky's algebraic cobordism spectrum, 2007 http://www.math.uiuc.edu/K-theory/0846

[124] A. Vishik, “Symmetric operations in algebraic cobordism”, Adv. Math., 213:2 (2007), 489–552 | DOI | MR | Zbl