Abstract
This paper provides some explicit expressions concerning the formal group laws of the following cohomology theories: BP, the Brown–Peterson cohomology, G(s), the cohomology theory obtained from BP by putting
Funding source: Shota Rustaveli National Science Foundation
Award Identifier / Grant number: DI/16/5-103/12
Funding source: Volkswagen Foundation
Award Identifier / Grant number: I/84 328
Funding statement: The first author was supported by Shota Rustaveli National Science Foundation (DI/16/5-103/12), and by Volkswagen Foundation (ref. I/84 328).
References
1 M. Bakuradze and S. Priddy, Transfer and complex oriented cohomology rings, Algebr. Geom. Topol. 3 (2003), 473–509. 10.2140/agt.2003.3.473Search in Google Scholar
2 M. Bakuradze and V. Vershinin, Morava K-theory rings for the dihedral, semidihedral and generalized quaternion groups in Chern classes, Proc. Amer. Math. Soc. 134 (2006), 12, 3707–3714. 10.1090/S0002-9939-06-08424-3Search in Google Scholar
3 V. M. Buchstaber, The ring of simple polytopes and differential equations (in Russian), Tr. Mat. Inst. Steklova 263 (2008), 18–43; translation in Proc. Steklov Inst. Math. 263 (2008), no. 1, 13–37. 10.1134/S0081543808040032Search in Google Scholar
4 V. M. Buchstaber, Complex cobordisms and formal groups (in Russian), Uspekhi Mat. Nauk 67 (2012), 5(407), 111–174; translation in Russian Math. Surveys 67 (2012), no. 5, 891–950. 10.1070/RM2012v067n05ABEH004809Search in Google Scholar
5 V. M. Buchstaber and A. N. Kholodov, Formal groups, functional equations and generalized cohomology theories (in Russian), Mat. Sb. 181 (1990), 1, 75–94; translation in Math. USSR-Sb. 69 (1991), no. 1, 77–97. Search in Google Scholar
6 P. Busato, Realization of Abel's universal formal group law, Math. Z. 239 (2002), 3, 527–561. 10.1007/s002090100323Search in Google Scholar
7 E. H. Brown, Jr and F. P. Peterson, A spectrum whose Zp cohomology is the algebra of reduced p-th powers, Topology 5 (1966), 149–154. 10.1016/0040-9383(66)90015-2Search in Google Scholar
8 M. Hazewinkel, Constructing formal groups. II. The global one-dimensional case, J. Pure Appl. Algebra 9 (1977), 2, 151–161. 10.1016/0022-4049(77)90062-7Search in Google Scholar
9 K. D. Kordzaya and R. G. Nadiradze, Elliptic genera of level n and umbral analysis (in Russian), Soobshch. Akad. Nauk Gruzin. SSR 135 (1989), 1, 41–44. Search in Google Scholar
10 R. Nadiradze, Formal group and cohomology theories, Doctor's degree dissertation, Tbilisi, 1995. Search in Google Scholar
11 S. P. Novikov, The methods of algebraic topology from the viewpoint of cobordism theory (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 4, 855–951; translation in Math. USSR-Izv. 1 (1967), no. 4, 827–913. 10.1142/9789814401319_0009Search in Google Scholar
12 D. Quillen, On the formal group laws of unoriented and complex cobordism theory, Bull. Amer. Math. Soc. 75 (1969), 1293–1298. 10.1142/9789812772107_0006Search in Google Scholar
13 D. C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres, Pure Appl. Math. 121, Academic Press, Orlando, 1986. Search in Google Scholar
14 Y. B. Rudyak, On Thom Spectra, Orientability, and Cobordism, Monogr. Math., Springer, Berlin, 1998. Search in Google Scholar
15 S. Roman, The Gould polynomials and the central factorial polynomials, The Umbral Calculus, Academic Press, New York (1984), 67–70. Search in Google Scholar
16 J. H. Silverman, The Arithmetic of Elliptic Curves, 2nd ed., Grad. Texts in Math. 106, Springer, New York, 2009. 10.1007/978-0-387-09494-6Search in Google Scholar
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