Complex cobordism and formal groups

V. M. Buchstaber

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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, infinitedimensional Lie algebras, and nilmanifolds are described. The survey contains key results and open problems.

Original languageEnglish
Pages (from-to)891-950
Number of pages60
JournalRussian Mathematical Surveys
Issue number5
Publication statusPublished - 2012
Externally publishedYes


  • Adams operations
  • Atiyah-Hirzebruch spectral sequence
  • Chern-Dold character
  • Hirzebruch genera
  • Landweber-Novikov algebra


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