Formal group law in topology

Summary

A formal group law over a commutative ring $R$ is a power series $F(x, y) = x + y + \cdots$ in two variables. It behaves like the addition of a group. In topology, every complex-oriented generalized cohomology theory $E$ carries such a law. The law expresses the first Chern class of a tensor product of line bundles through the Chern classes of the factors. Ordinary cohomology gives the additive law $x + y$ and complex K-theory gives a multiplicative law. Quillen's theorem says that complex cobordism carries the universal formal group law, which links stable homotopy theory to the algebraic geometry of formal groups.