2009

Cohomology and Hodge Theory on Symplectic Manifolds: I

Tseng, Li-Sheng, Yau, Shing-Tung

Understand

We introduce new finite-dimensional cohomologies on symplectic manifolds.

Each exhibits Lefschetz decomposition and contains a unique harmonic representative within each class.
Associated with each cohomology is a primitive cohomology defined purely on the space of primitive forms.
We identify the dual currents of lagrangians and more generally coisotropic submanifolds with elements of a primitive cohomology, which dualizes to a homology on coisotropic chains.

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L.-S. Tseng and S.-T. Yau, Cohomology and Hodge theory on symplectic manifolds: II
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