Complex cobordism
= Complex cobordism
{title2=$MU^*(X)=\Omega_U^*(X)$}
Complex cobordism is the <generalized cohomology theory> represented by the stable Thom spaces of universal complex vector bundles. Its geometric cycles use maps with chosen stable complex normal data. Its complex <Thom classes> give <Chern classes in complex cobordism>, and proper oriented maps have a <Gysin map in complex cobordism>.