On a dual submanifold homomorphism

In this paper we develop a technique to study the homomorphisma: MU _* (B U₁)→M U_*?2 (B U₁) defined by assigning to the class off: M→B U ₁ the class off _oi: N→B U₁, wherei: N→M is the submanifold dual tof*(γ₁)?f*(γ₁), and γ₁→B U is the 3 universal line boundle. So that we can present a (σ_n), where σ_nis the class of the classifying map of the canonical line boundle overC P ⁿ, in terms of the σ_i’s and chosen generators of Π_★(M U).