Flux Conjecture on Symplectic Submanifolds

Abstract

Let $(M, \omega)$ be a closed symplectic $2n$-dimensional manifold. According to the well-known result by Donaldson [5] there exist $2m$-dimensional symplectic submanifolds $(V^{2m}, \omega)$ of $(M, \omega), 1 \leq m \leq n - 1$, with $(m − 1)$-equivalent inclusions. In this paper, we have found a relation between the flux group and the kernel of the Lefschetz map. We have present also some properties of the flux groups for all symplectic $2m$-submanifolds $(V^{2m}, \omega)$ where $2 \leq m \leq n - 1$.