Dolbeault and $J$-invariant cohomologies on almost complex manifolds

TL;DR

This paper explores the relationship between $J$-invariant and Dolbeault cohomologies on almost complex manifolds, providing conditions for their isomorphism and extending existing results to solvmanifolds with examples.

Contribution

It establishes necessary and sufficient conditions for the isomorphism between $J$-invariant and Dolbeault cohomologies and extends cohomology computations to solvmanifolds.

Findings

Conditions for cohomology isomorphism are identified.

Extension of cohomology computation methods to solvmanifolds.

Multiple examples illustrating the theoretical results.

Abstract

In this paper we relate the cohomology of $J$-invariant forms to the Dolbeault cohomology of an almost complex manifold. We find necessary and sufficient condition for the inclusion of the former into the latter to be true up to isomorphism. We also extend some results obtained by J. Cirici and S.O. Wilson about the computation of the left-invariant cohomology of nilmanifolds to the setting of solvmanifolds. Several examples are given.