Gromov K-area and jumping curves in CP^n

We give here some extensions of Gromov’s and Polterovich’s theorems on $\text{karea}$ of ${\mathbb{C}\mathbb{P}}^n$, 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 ${\mathbb{C}\mathbb{P}}^n$, and as an upshot we prove a new symplectic geometric theorem on these jumping curves.