On Cohomological Decomposability of Almost-K\"ahler Structures

TL;DR

This paper investigates the cohomological properties of almost-Kähler manifolds, focusing on J-invariant and J-anti-invariant subgroups, especially those satisfying Lefschetz properties and on solvmanifolds with invariant structures.

Contribution

It provides new insights into the cohomological decomposability of almost-Kähler structures, particularly in relation to Lefschetz properties and solvmanifolds.

Findings

Analysis of J-invariant and J-anti-invariant cohomology subgroups

Identification of conditions under which almost-Kähler manifolds satisfy Lefschetz properties

Study of cohomological decomposability on solvmanifolds with invariant structures

Abstract

We study the J-invariant and J-anti-invariant cohomological subgroups of the de Rham cohomology of a compact manifold M endowed with an almost-K\"ahler structure (J, \omega, g). In particular, almost-K\"ahler manifolds satisfying a Lefschetz type property, and solvmanifolds endowed with left-invariant almost-complex structures are investigated.