Gromov K-area and jumping curves in CP^n

We give here some extensions of Gromov's and Polterovich's theorems on $\karea$ of $\mathbb{CP} ^{n}$, particularly in the symplectic and Hamiltonian context. Our main methods involve Gromov-Witten theory, and some connections with Bott periodicity, and loop groups. The argument is closely connected with study of jumping curves in $\mathbb{CP} ^{n}$, and as an upshot we prove a new symplectic geometric theorem on these jumping curves.