Complex-oriented cohomology theory

In algebraic topology, a complex-orientable cohomology theory is a multiplicative cohomology theory E such that the restriction map E 2 ( C P ∞ ) → E 2 ( C P 1 ) {\displaystyle E^{2}(\mathbb {C} \mathbf {P} ^{\infty })\to E^{2}(\mathbb {C} \mathbf {P} ^{1})} is surjective. An element of E 2 ( C P ∞ ) {\displaystyle E^{2}(\mathbb {C} \mathbf {P} ^{\infty })} that restricts to the canonical generator of the reduced theory E ~ 2 ( C P 1 ) {\displaystyle {\widetilde {E}}^{2}(\mathbb {C} \mathbf {P} ^{1})} is called a complex orientation.

Source: Wikipedia — Complex-oriented cohomology theory (CC BY-SA 4.0)