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 $(X,J,g,\omega )$ with $J$ ${\mathcal{C}}^{\infty }$-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.

References in corpus (6)

• New aspects of the ddc-lemma
• On the cohomology of almost-complex manifolds
• A Frölicher-type inequality for generalized complex manifolds
• On the cohomology of almost complex and symplectic manifolds and proper surjective maps
• Cohomologies of locally conformally symplectic manifolds and solvmanifolds
• On non-Kähler degrees of complex manifolds

Cited by in corpus (2)

• Some Morse-type inequalities for symplectic manifolds
• On second non-HLC degree of closed symplectic manifold