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arXiv · 1601.08146

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

Nicoletta Tardini·Adriano Tomassini
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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.

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Nicoletta Tardini, Adriano Tomassini. 2016-01-29. On the cohomology of almost complex and symplectic manifolds and proper surjective maps. https://doi.org/10.1142/s0129167x16501032

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