Symplectic cohomologies and deformations

Abstract

In this note we study the behavior of symplectic cohomology groups under symplectic deformations. Moreover, we show that for compact almost-Kähler manifolds (X, J, g, ω) with J C ∞ -pure and full the space of de Rham harmonic forms is contained in the space of symplectic-Bott-Chern harmonic forms. Furthermore, we prove that the second non-HLC degree measures the gap between the de Rham and the symplectic-Bott-Chern harmonic forms.

On second non-HLC degree of closed symplectic manifold

“…when the manifold X is understood. In [3,15] Angella and Tomassini, starting from a purely algebraic point of view, introduce on a compact symplectic manifold (X 2n , ω) the following non-negative integers…”

Some Morse-type inequalities for symplectic manifolds

“…Remark 1. The dimensions of the d + d Λ and dd Λ groups can vary under homotopy of the symplectic form [26].…”