Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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N. Tardini - A. Tomassini

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

created by tardini on 24 Jan 2019


Published Paper

Inserted: 24 jan 2019
Last Updated: 24 jan 2019

Journal: Internat. J. Math.
Volume: 27
Number: 12
Pages: 1650103 (20 pages)
Year: 2016

ArXiv: 1601.08146 PDF


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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