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Uspekhi Mat. Nauk, 2012, Volume 67, Issue 5(407), Pages 111–174 (Mi umn9496)  

This article is cited in 6 scientific papers (total in 7 papers)

Complex cobordism and formal groups

V. M. Buchstaber

Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: This paper surveys the current state of the theory of cobordism, focusing on geometric and universal properties of complex cobordism, the Landweber–Novikov algebra, and the formal group law of geometric cobordisms. The relationships with $K$-theory, algebraic cycles, formal group laws, compact Lie group actions on manifolds, toric topology, infinite-dimensional Lie algebras, and nilmanifolds are described. The survey contains key results and open problems.
Bibliography: 124 titles.

Keywords: Landweber–Novikov algebra, Adams operations, Chern–Dold character, Atiyah–Hirzebruch spectral sequence, Hirzebruch genera.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00694
Ministry of Education and Science of the Russian Federation 11.G34.31.0053


DOI: https://doi.org/10.4213/rm9496

Full text: PDF file (997 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2012, 67:5, 891–950

Bibliographic databases:

Document Type: Article
UDC: 515.164.24+515.171.36+512.741
MSC: 57R77, 55N22
Received: 02.09.2012

Citation: V. M. Buchstaber, “Complex cobordism and formal groups”, Uspekhi Mat. Nauk, 67:5(407) (2012), 111–174; Russian Math. Surveys, 67:5 (2012), 891–950

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. M. Bakuradze, “Computing the Krichever genus”, J. Homotopy Relat. Struct., 9:1 (2014), 85–93  crossref  mathscinet  zmath  isi  elib
    3. V. M. Bukhshtaber, E. Yu. Bunkova, “Universalnaya formalnaya gruppa, opredelyayuschaya ellipticheskuyu funktsiyu urovnya 3”, Chebyshevskii sb., 16:2 (2015), 66–78  mathnet  elib
    4. V. M. Buchstaber, A. V. Ustinov, “Coefficient rings of formal group laws”, Sb. Math., 206:11 (2015), 1524–1563  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. E. Yu. Bunkova, V. M. Buchstaber, A. V. Ustinov, “Coefficient rings of Tate formal groups determining Krichever genera”, Proc. Steklov Inst. Math., 292 (2016), 37–62  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. G. D. Solomadin, Yu. M. Ustinovskiy, “Projective toric polynomial generators in the unitary cobordism ring”, Sb. Math., 207:11 (2016), 1601–1624  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. Bakuradze M., Jibladze M., “Some explicit expressions concerning BP”, Georgian Math. J., 23:2 (2016), 157–167  crossref  mathscinet  zmath  isi  elib  scopus
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