On the cohomology of almost complex and symplectic manifolds and proper surjective maps

Abstract

Let $(X,J)$ be an almost-complex manifold. In \cite{li-zhang} Li and Zhang introduce $H^{(p,q),(q,p)}_J(X)_{\rr}$ as the cohomology subgroups of the $(p+q)$-th de Rham cohomology group formed by classes represented by real pure-type forms. Given a proper, surjective, pseudo-holomorphic map between two almost-complex manifolds we study the relationship among such cohomology groups. Similar results are proven in the symplectic setting for the cohomology groups introduced in \cite{tsengyauI} by Tseng and Yau and a new characterization of the Hard Lefschetz condition in dimension $4$ is provided.

References in corpus (3)

• On the cohomology of almost-complex manifolds
• Quantitative and qualitative cohomological properties for non-Kähler manifolds
• A Frölicher-type inequality for generalized complex manifolds

Cited by in corpus (2)

• Symplectic cohomologies and deformations
• On second non-HLC degree of closed symplectic manifold