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