V. M. Buchstaber, “Complex cobordism and formal groups”, Russian Math. Surveys, 67:5 (2012), 891

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Russian Mathematical Surveys, 2012, Volume 67, Issue 5, Pages 891–950
DOI: https://doi.org/10.1070/RM2012v067n05ABEH004809 (Mi rm9496)

This article is cited in 15 scientific papers (total in 16 papers)

Complex cobordism and formal groups

V. M. Buchstaber

Steklov Mathematical Institute of the Russian Academy of Sciences

English version PDF (933 kB) Citations (16) Russian version article

References:

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DOI: https://doi.org/10.1070/RM2012v067n05ABEH004809

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

$K$ -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

Received: 02.09.2012

Bibliographic databases:

Document Type: Article

UDC: 515.164.24+515.171.36+512.741

MSC: 57R77, 55N22

Language: English

Original paper language: Russian

Citation: V. M. Buchstaber, “Complex cobordism and formal groups”, Russian Math. Surveys, 67:5 (2012), 891–950

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/rm9496

https://doi.org/10.1070/RM2012v067n05ABEH004809

https://www.mathnet.ru/eng/rm/v67/i5/p111

This publication is cited in the following 16 articles:

V. M. Buchstaber, A. P. Veselov, “Chern–Dold character in complex cobordisms and theta divisors”, Adv. Math., 449 (2024), 109720
V. M. Buchstaber, A. P. Veselov, “Todd Polynomials and Hirzebruch Numbers”, Proc. Steklov Inst. Math., 325 (2024), 74–85
T. E. Panov, G. S. Chernykh, “ $SU$ -linear operations in complex cobordism and the $c_1$ -spherical bordism theory”, Izv. Math., 87:4 (2023), 768–797
V. M. Buchstaber, “Vladimir Abramovich Rokhlin and algebraic topology”, Contemp. Math., 772 (2021), 33–68
V. M. Buchstaber, “Partially framed manifolds and loop spaces on the group $\operatorname{SU}(2)$ ”, Russian Math. Surveys, 75:4 (2020), 782–784
I. Yu. Limonchenko, T. E. Panov, G. S. Chernykh, “ $SU$ -bordism: structure results and geometric representatives”, Russian Math. Surveys, 74:3 (2019), 461–524
E. Yu. Bunkova, “Universal Formal Group for Elliptic Genus of Level $N$ ”, Proc. Steklov Inst. Math., 305 (2019), 33–52
Malkhaz Bakuradze, Vladimir V. Vershinin, “On Addition Theorems Related to Elliptic Integrals”, Proc. Steklov Inst. Math., 305 (2019), 22–32
V. M. Buchstaber, “Cobordisms, manifolds with torus action, and functional equations”, Proc. Steklov Inst. Math., 302 (2018), 48–87
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
G. D. Solomadin, Yu. M. Ustinovskiy, “Projective toric polynomial generators in the unitary cobordism ring”, Sb. Math., 207:11 (2016), 1601–1624
Bakuradze M., Jibladze M., “Some explicit expressions concerning BP”, Georgian Math. J., 23:2 (2016), 157–167
V. M. Bukhshtaber, E. Yu. Bunkova, “Universalnaya formalnaya gruppa, opredelyayuschaya ellipticheskuyu funktsiyu urovnya 3”, Chebyshevskii sb., 16:2 (2015), 66–78
V. M. Buchstaber, A. V. Ustinov, “Coefficient rings of formal group laws”, Sb. Math., 206:11 (2015), 1524–1563
M. Bakuradze, “Computing the Krichever genus”, J. Homotopy Relat. Struct., 9:1 (2014), 85–93
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

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

Statistics & downloads:
Abstract page:	1476
Russian version PDF:	609
English version PDF:	72
References:	106
First page:	63

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