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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)
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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 $K$-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
Russian version:
Uspekhi Matematicheskikh Nauk, 2012, Volume 67, Issue 5(407), Pages 111–174
DOI: https://doi.org/10.4213/rm9496
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”, Uspekhi Mat. Nauk, 67:5(407) (2012), 111–174; Russian Math. Surveys, 67:5 (2012), 891–950
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:88
    First page:63
     
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