Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

Online
ISSN
1572-9176
See all formats and pricing
More options …
Volume 26, Issue 2

Issues

On formal group laws over the quotients of Lazard’s ring

Malkhaz Bakuradze
  • Corresponding author
  • Faculty of Exact and Natural Sciences, A. Razmadze Mathematical Institute, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Vladimir Vershinin
  • Departement des Sciences Mathematiques, Universitè de Montpellier, Montpellier, France; and Sobolev Institute of Mathematics, Russia
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2019-04-09 | DOI: https://doi.org/10.1515/gmj-2019-2022

Abstract

We present a formal power series Aijxiyj over the Lazard ring Λ and the formal group laws Fn, n2, over the quotient rings of Λ. For each Fn, we construct a complex cobordism theory with singularities with the coefficient ring [p1,,p2n], with parameters pi, |pi|=2i.

Keywords: Lazard ring; formal group law

MSC 2010: 33E05; 55N22

Dedicated to Academician Nodar Berikashvili on the occasion of his 90th birthday

References

  • [1]

    N.-A. Baas, On bordism theory of manifolds with singularities, Math. Scand. 33 (1973), 279–302. CrossrefGoogle Scholar

  • [2]

    M. Bakuradze, The formal groups of Bukhshtaber, Krichever, and Nadiradze coincide (in Russian), Uspekhi Mat. Nauk 68 (2013), no. 3(411), 189–190; translation in Russian Math. Surveys 68 (2013), no. 3, 571–573. Google Scholar

  • [3]

    M. Bakuradze, On the Buchstaber formal group law and some related genera (in Russian), Tr. Mat. Inst. Steklova 286 (2014), 7–21; translation in Proc. Steklov Inst. Math. 286 (2014), no. 1, 1–15. Google Scholar

  • [4]

    M. Bakuradze, Computing the Krichever genus, J. Homotopy Relat. Struct. 9 (2014), no. 1, 85–93. CrossrefGoogle Scholar

  • [5]

    M. Bakuradze and V. Vershinin, On addition theorems related to elliptic integrals, Proc. Steklov Inst. Math., to appear. Google Scholar

  • [6]

    V. M. Buchstaber, Functional equations that are associated with addition theorems for elliptic functions, and two-valued algebraic groups (in Russian), Uspekhi Mat. Nauk 45 (1990), no. 3(273), 185–186; translation in Proc. Steklov Inst. Math. 286 (2014), no. 1, 1–15. Google Scholar

  • [7]

    V. M. Buchstaber and A. N. Kholodov, Formal groups, functional equations and generalized cohomology theories (in Russian), Mat. Sb. 181 (1990), no. 1, 75–94; translation in Math. USSR-Sb. 69 (1991), no. 1, 77–97. Google Scholar

  • [8]

    V. M. Buchstaber and T. E. Panov, Toric Topology, Math. Surveys Monogr. 204, American Mathematical Society, Providence, 2015. Google Scholar

  • [9]

    M. Hazewinkel, Formal Groups and Applications, Pure Appl. Math. 78, Academic Press, New York, 1978. Google Scholar

  • [10]

    M. Lazard, Sur les groupes de Lie formels à un paramètre, Bull. Soc. Math. France 83 (1955), 251–274. Google Scholar

  • [11]

    R. Nadiradze, Formal group and cohomology theories, Dissertation for the Doctoral Science Degree, Tbilisi, 1995. Google Scholar

  • [12]

    S. P. Novikov, Methods of algebraic topology from the point of view of cobordism theory (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), no. 4, 855–951; translation in Math. USSR-Izv. 1 (1967), no. 4, 827–913. Google Scholar

  • [13]

    S. Ochanine, Sur les genres multiplicatifs définis par des intégrales elliptiques, Topology 26 (1987), no. 2, 143–151. CrossrefGoogle Scholar

  • [14]

    D. Quillen, On the formal group laws of unoriented and complex cobordism theory, Bull. Amer. Math. Soc. 75 (1969), 1293–1298. CrossrefGoogle Scholar

  • [15]

    V. V. Vershinin, Cobordisms and Spectral Sequences, Transl. Math. Monogr. 130, American Mathematical Society, Providence, 1993. Google Scholar

About the article

Received: 2018-09-27

Accepted: 2018-12-26

Published Online: 2019-04-09

Published in Print: 2019-06-01


The first author was supported by CNRS PICS N 7736, and by Shota Rustaveli NSF grant 217-614. The second author was supported by CNRS PICS N 7736.


Citation Information: Georgian Mathematical Journal, Volume 26, Issue 2, Pages 159–164, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2019-2022.

Export Citation

© 2019 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in