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  "body": "\n## Summary\n\nComplex cobordism $MU^*$ is the [[generalized cohomology theory|H28PSZR7XG]] represented by the Thom spectrum $MU$ of the universal complex vector bundles.\nIts coefficient ring is the cobordism ring of stably complex manifolds, a polynomial ring over $\\Z$ with one generator in each positive even degree.\nBy a theorem of Quillen this ring carries the universal formal group law.\nThis link makes complex cobordism the central theory of modern stable homotopy theory.\n\n## Explanations\n\n### L1 human\n\nOn a point, complex cobordism is built from closed manifolds with a complex structure on their stable normal bundle.\nTwo such manifolds give the same class when together they bound such a manifold.\nThe theory extends this count of manifolds to a cohomology theory defined for all spaces.\nIt is the most refined of the complex-oriented cohomology theories, in the sense that it maps to each of them.\nFor example, the coefficient group $\\pi_2(MU)$ is $\\Z$, generated by the Riemann sphere $\\C P^1$.\n",
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