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Izv. Akad. Nauk SSSR Ser. Mat., 1975, Volume 39, Issue 5, Pages 1044–1064 (Mi izv2079)  

This article is cited in 10 scientific papers (total in 12 papers)

Two-valued formal groups. Algebraic theory and applications to cobordism. I

V. M. Buchstaber


Abstract: An axiomatic definition is given for the notion of a two-valued formal group. The coalgebra and the generalized translation associated with a two-valued formal group are then defined and studied. A complete classification is obtained for two-valued formal groups over $Q$-algebras.
Bibliography: 11 titles.

Full text: PDF file (1783 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1975, 9:5, 987–1006

Bibliographic databases:

UDC: 519.4
MSC: Primary 13J05, 14L05; Secondary 22E99, 57D90
Received: 02.12.1974

Citation: V. M. Buchstaber, “Two-valued formal groups. Algebraic theory and applications to cobordism. I”, Izv. Akad. Nauk SSSR Ser. Mat., 39:5 (1975), 1044–1064; Math. USSR-Izv., 9:5 (1975), 987–1006

Citation in format AMSBIB
\Bibitem{Buc75}
\by V.~M.~Buchstaber
\paper Two-valued formal groups. Algebraic theory and applications to cobor\-dism.~I
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1975
\vol 39
\issue 5
\pages 1044--1064
\mathnet{http://mi.mathnet.ru/izv2079}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=469927}
\zmath{https://zbmath.org/?q=an:0324.14010}
\transl
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 5
\pages 987--1006
\crossref{https://doi.org/10.1070/IM1975v009n05ABEH001514}


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    This publication is cited in the following articles:
    1. V. M. Buchstaber, “Two-valued formal groups. Algebraic theory and applications to cobordism. II”, Math. USSR-Izv., 10:2 (1976), 271–308  mathnet  crossref  mathscinet  zmath
    2. V. M. Bukhshtaber, “Dvuznachnye formalnye gruppy v apparate teorii kobordizmov”, UMN, 32:2(194) (1977), 205–206  mathnet  mathscinet  zmath
    3. V. M. Buchstaber, “Topological applications of the theory of two-valued formal groups”, Math. USSR-Izv., 12:1 (1978), 125–177  mathnet  crossref  mathscinet  zmath
    4. V. M. Buchstaber, A. V. Shokurov, “The Landweber–Novikov algebra and formal vector fields on the line”, Funct. Anal. Appl., 12:3 (1978), 159–168  mathnet  crossref  mathscinet  zmath
    5. A. N. Kholodov, “Algebraic theory of multi-valued formal groups”, Math. USSR-Sb., 42:2 (1982), 265–285  mathnet  crossref  mathscinet  zmath
    6. D. I. Gurevich, “On many-valued Lie groups”, Russian Math. Surveys, 39:6 (1984), 213–214  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. V. M. Buchstaber, A. N. Kholodov, “Groups of formal diffeomorphisms of the superline, generating functions for sequences of polynomials, and functional equations”, Math. USSR-Izv., 35:2 (1990), 277–305  mathnet  crossref  mathscinet  zmath
    8. V. M. Buchstaber, A. N. Kholodov, “Formal groups, functional equations and generalized cohomology theories”, Math. USSR-Sb., 69:1 (1991), 77–97  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. A. A. Bolibrukh, A. P. Veselov, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, S. P. Novikov, T. E. Panov, Yu. M. Smirnov, “Viktor Matveevich Buchstaber (on his 60th birthday)”, Russian Math. Surveys, 58:3 (2003), 627–635  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    10. I. K. Babenko, “Algebra, geometry, and topology of the substitution group of formal power series”, Russian Math. Surveys, 68:1 (2013), 1–68  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. A. M. Vershik, A. P. Veselov, A. A. Gaifullin, B. A. Dubrovin, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, D. V. Millionshchikov, S. P. Novikov, T. E. Panov, A. G. Sergeev, I. A. Taimanov, “Viktor Matveevich Buchstaber (on his 70th birthday)”, Russian Math. Surveys, 68:3 (2013), 581–590  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. V. M. Buchstaber, A. P. Veselov, “Conway topograph, $\mathrm{PGL}_2(\pmb{\mathbb Z})$-dynamics and two-valued groups”, Russian Math. Surveys, 74:3 (2019), 387–430  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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