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Mathematics of the USSR-Izvestiya, 1975, Volume 9, Issue 5, Pages 987–1006
DOI: https://doi.org/10.1070/IM1975v009n05ABEH001514
(Mi im2079)
 

This article is cited in 13 scientific papers (total in 15 papers)

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

V. M. Buchstaber
References:
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.
Received: 02.12.1974
Bibliographic databases:
Document Type: Article
UDC: 519.4
MSC: Primary 13J05, 14L05; Secondary 22E99, 57D90
Language: English
Original paper language: Russian
Citation: V. M. Buchstaber, “Two-valued formal groups. Algebraic theory and applications to cobordism. I”, 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 Math. USSR-Izv.
\yr 1975
\vol 9
\issue 5
\pages 987--1006
\mathnet{http://mi.mathnet.ru/eng/im2079}
\crossref{https://doi.org/10.1070/IM1975v009n05ABEH001514}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=469927}
\zmath{https://zbmath.org/?q=an:0324.14010}
Linking options:
  • https://www.mathnet.ru/eng/im2079
  • https://doi.org/10.1070/IM1975v009n05ABEH001514
  • https://www.mathnet.ru/eng/im/v39/i5/p1044
    Cycle of papers
    This publication is cited in the following 15 articles:
    1. V. M. Buchstaber, F. Yu. Popelenskii, “Cohomology of Hopf algebras and Massey products”, Russian Math. Surveys, 79:4 (2024), 567–648  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. V. M. Buchstaber, A. Yu. Vesnin, “$n$-valued groups, branched coverings and hyperbolic 3-manifolds”, Sb. Math., 215:11 (2024), 1441–1467  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    3. V. M. Buchstaber, A. P. Veselov, A. A. Gaifullin, “Classification of involutive commutative two-valued groups”, Russian Math. Surveys, 77:4 (2022), 651–727  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. 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  zmath  adsnasa  isi  elib
    5. 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
    6. 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
    7. 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
    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. 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
    10. D. I. Gurevich, “On many-valued Lie groups”, Russian Math. Surveys, 39:6 (1984), 213–214  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. A. N. Kholodov, “Algebraic theory of multi-valued formal groups”, Math. USSR-Sb., 42:2 (1982), 265–285  mathnet  crossref  mathscinet  zmath
    12. 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
    13. 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
    14. V. M. Bukhshtaber, “Dvuznachnye formalnye gruppy v apparate teorii kobordizmov”, UMN, 32:2(194) (1977), 205–206  mathnet  mathscinet  zmath
    15. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:672
    Russian version PDF:226
    English version PDF:42
    References:94
    First page:3
     
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