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Chern class
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===Generalized cohomology theories=== There is a generalization of the theory of Chern classes, where ordinary cohomology is replaced with a [[generalized cohomology theory]]. The theories for which such generalization is possible are called ''[[Complex cobordism#Formal group laws|complex orientable]]''. The formal properties of the Chern classes remain the same, with one crucial difference: the rule which computes the first Chern class of a tensor product of line bundles in terms of first Chern classes of the factors is not (ordinary) addition, but rather a [[formal group law]].
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