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Doulbeault and J-invariant Cohomologies on Almost Complex Manifolds

TitleDoulbeault and J-invariant Cohomologies on Almost Complex Manifolds
Publication TypeJournal Article
Year of Publication2021
AuthorsSillari, L, Tomassini, A
JournalComplex Analysis and Operator Theory
Date Published09/2021
Type of ArticleArticle
Other NumbersArticle number: 112
KeywordsAlmost Complex Manifolds; Cohomology of Lie Algebra; Compact four-manifold; Dolbeault Cohomology; Frölicher Spectral Sequence; Solvmanifold

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.


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