Cohomology and Hodge Theory on Symplectic Manifolds: I

Li-Sheng Tseng; Shing-Tung Yau

Cohomology and Hodge Theory on Symplectic Manifolds: I

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arxiv 0909.5418 v2 pith:SQ2VP5IX submitted 2009-09-29 math.SG hep-thmath.DG

Li-Sheng Tseng , Shing-Tung Yau This is my paper · ORCID

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keywords cohomologyprimitivecoisotropicmanifoldssymplecticassociatedchainsclass

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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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Boundary framings for locally conformally symplectic four-manifolds
math.AT 2025-02 reject novelty 5.0 of 10

The paper proposes a rational homotopy model for a classifying space of locally conformally symplectic four-manifolds and a cobordism category of three-manifolds with Omega^2 S^2-bundle framings, but the standalone te...

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