Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter March 17, 2016

Some explicit expressions concerning BP

Malkhaz Bakuradze and Mamuka Jibladze

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 vi=0 for all i ≥ 1 with is, the Morava K-theory and the Abel cohomology. The coefficient rings of Weierstrass universal elliptic curve formal group law are computed in low dimensions.

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. Search 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. Search 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. Search 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. Search 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. Search 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. Search in Google Scholar

8 M. Hazewinkel, Constructing formal groups. II. The global one-dimensional case, J. Pure Appl. Algebra 9 (1977), 2, 151–161. Search 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. Search 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. Search 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. Search in Google Scholar

Received: 2014-7-24
Revised: 2015-3-8
Accepted: 2015-3-27
Published Online: 2016-3-17
Published in Print: 2016-6-1

© 2016 by De Gruyter