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Symplectic harmonicity and generalized c...
Ugarte, Luis...

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Symplectic harmonicity and generalized coeffective cohomologies by Ugarte, Luis ( Author )
Lemonjar Open Access
Australian National University
01-09-2023
Relations between the symplectically harmonic cohomology and the coeffective cohomology of a symplectic manifold are obtained. This is achieved through a generalization of the latter, which in addition allows us to provide a coeffective version of the filtered cohomologies introduced by C.-J. Tsai, L.-S. Tseng and S.-T. Yau. We construct closed (simply connected) manifolds endowed with a family of symplectic forms $\omega_t$ such that the dimensions of these symplectic cohomology groups vary with respect to $t$. A complete study of these cohomologies is given for 6-dimensional symplectic nilmanifolds, and concrete examples with special cohomological properties are obtained on an $8$-dimensional solvmanifold and on 2-step nilmanifolds in higher dimensions.
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Article
pdf
29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1404.6777
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