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arXiv · 1404.6777

Symplectic harmonicity and generalized coeffective cohomologies

Luis Ugarte·Raquel Villacampa
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Abstract

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 $ω_t$ 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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Luis Ugarte, Raquel Villacampa. 2018-07-17. Symplectic harmonicity and generalized coeffective cohomologies. https://arxiv.org/abs/1404.6777

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