A Module Structure on the Symplectic Floer Cohomology

Abstract

The aim of this paper is to offer an affirmative answer to the Floer conjectures in [2, p. 589] which states that there is a module structure on the Z 2 N -graded symplectic Floer cohomology for monotone symplectic manifolds. By constructing a Z-graded symplectic Floer cohomology as an integral lift of the Z 2 N -graded symplectic Floer cohomology, we gain control of the holomorphic bubbling spheres. This makes a module structure on the Z-graded Floer cohomology. There is a spectral sequence with E 1 *,* given by the Z-graded symplectic Floer cohomology. Such a spectral sequence converges to the Z 2 N -graded symplectic Floer cohomology. Hence we induce a module structure for the Z 2 N -graded symplectic Floer cohomology by the spectral sequence and algebraic topology methods.