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  "body": "\n## Summary\n\nA formal group law over a commutative ring $R$ is a power series $F(x, y) = x + y + \\cdots$ in two variables.\nIt behaves like the addition of a group.\nIn topology, every complex-oriented [[generalized cohomology theory|H28PSZR7XG]] $E$ carries such a law.\nThe law expresses the first Chern class of a tensor product of line bundles through the Chern classes of the factors.\nOrdinary cohomology gives the additive law $x + y$ and complex K-theory gives a multiplicative law.\n[[Quillen's theorem|4E518M24MA]] says that [[complex cobordism|5CZHFNY9F3]] carries the universal formal group law, which links stable homotopy theory to the algebraic geometry of formal groups.\n\n## Explanations\n\n### L1 human\n\nFor complex line bundles, the first Chern class of $L_1 \\otimes L_2$ is $c_1(L_1) + c_1(L_2)$ in ordinary cohomology.\nIn other cohomology theories the rule is no longer plain addition but a power series, such as $x + y + \\beta x y$ in K-theory.\nSuch a power series still acts like addition: it is commutative and associative and has $0$ as a neutral element.\nThis \"twisted addition\" is a formal group law.\nIts shape records a lot about the cohomology theory, and the study of these laws by height leads to chromatic homotopy theory.\n",
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