On the cohomology of almost-complex manifolds

TL;DR

This paper investigates the relationship between the cohomology of almost-complex manifolds and their structures, extending previous work to analyze semi-Kähler structures and their cohomological properties.

Contribution

It applies existing methods to explore the cohomology and semi-Kähler cone structures on almost-complex manifolds, advancing understanding of their geometric and topological properties.

Findings

Extended cohomological analysis to semi-Kähler structures.

Linked cohomology properties with almost-complex structures.

Provided new insights into semi-Kähler cone geometry.

Abstract

Following T.-J. Li, W. Zhang [Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.], we continue to study the link between the cohomology of an almost-complex manifold and its almost-complex structure. In particular, we apply the same argument in [T.-J. Li, W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.] and the results obtained by D. Sullivan in [Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math.] to study the cone of semi-K\"ahler structures on a compact semi-K\"ahler manifold.