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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 1, Pages 130–184 (Mi izv1694)  

This article is cited in 7 scientific papers (total in 8 papers)

Topological applications of the theory of two-valued formal groups

V. M. Buchstaber


Abstract: The Pontryagin classes of real vector bundles are constructed in selfconjugate cobordism theory. In terms of these classes a construction of the two-valued formal group in cobordism is carried out and a topological interpretation of the main results of the algebraic theory of two-valued formal groups is given.
The ring $Л^{ *}(X)=\operatorname{Hom}_{A^U}(U^*(M\operatorname{Sp}),U_*(X))$ is computed for the basic nontrivial cases where $X=(point)$ and $X=\mathbf CP(\infty)$. An effective description of the cobordism classes of Stong manifolds is given, and a number of problems on the cobordism classes associated with the universal Pontryagin classes are solved. The principal characteristics of the cobordism ring of selfconjugate manifolds are calculated, including the image of this ring in the cobordism ring of nonorientable manifolds.
Bibliography: 29 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1978, 12:1, 125–177

Bibliographic databases:

UDC: 519.4
MSC: Primary 14L05; Secondary 57D90
Received: 27.07.1976

Citation: V. M. Buchstaber, “Topological applications of the theory of two-valued formal groups”, Izv. Akad. Nauk SSSR Ser. Mat., 42:1 (1978), 130–184; Math. USSR-Izv., 12:1 (1978), 125–177

Citation in format AMSBIB
\Bibitem{Buc78}
\by V.~M.~Buchstaber
\paper Topological applications of the theory of two-valued formal groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 1
\pages 130--184
\mathnet{http://mi.mathnet.ru/izv1694}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=494160}
\zmath{https://zbmath.org/?q=an:0384.57018|0402.57032}
\transl
\jour Math. USSR-Izv.
\yr 1978
\vol 12
\issue 1
\pages 125--177
\crossref{https://doi.org/10.1070/IM1978v012n01ABEH001843}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. P. Golubyatnikov, “Bordism rings with split normal bundles”, Russian Math. Surveys, 34:6 (1979), 172–176  mathnet  crossref  mathscinet  zmath
    2. R. G. Nadiradze, “Involutions on Stong manifolds and their application in cobordism theory”, Russian Math. Surveys, 35:3 (1980), 264–267  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. M. Buchstaber, A. N. Kholodov, “Topological constructions connected with many-valued formal groups”, Math. USSR-Izv., 20:1 (1983), 1–25  mathnet  crossref  mathscinet  zmath
    4. V. P. Golubyatnikov, “Manifolds with split (into halves) stable normal bundles in phase spaces”, Funct. Anal. Appl., 18:2 (1984), 139–140  mathnet  crossref  mathscinet  zmath  isi
    5. V. M. Buchstaber, K. E. Feldman, “An addition formula for the first semi-integral Pontryagin class in complex cobordism”, Russian Math. Surveys, 52:6 (1997), 1287–1288  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. V. M. Buchstaber, K. E. Feldman, “The index of an equivariant vector field and addition theorems for Pontryagin classes”, Izv. Math., 64:2 (2000), 223–247  mathnet  crossref  crossref  mathscinet  zmath  isi
    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. A. A. Gaifullin, “Computation of characteristic classes of a manifold from a triangulation of it”, Russian Math. Surveys, 60:4 (2005), 615–644  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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