Gromov K-area and jumping curves in CP^n

TL;DR

This paper extends Gromov's and Polterovich's theorems on the Gromov K-area of complex projective spaces, using Gromov-Witten theory and loop group connections to explore symplectic and Hamiltonian properties.

Contribution

It introduces new extensions of existing theorems on Gromov K-area in CP^n, linking them with jumping curves and symplectic geometry.

Findings

Extended Gromov's and Polterovich's theorems on K-area

Established new results on jumping curves in CP^n

Connected Gromov-Witten theory with symplectic geometry

Abstract

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.