Cohomology and Hodge Theory on Symplectic Manifolds: I

2009/09/30 by Li-Sheng Tseng, Shing-Tung Yau · 2 citations
Mathematics · Physics and Astronomy · #math.SG #hep-th #math.DG

paper · pdf

published as J. Differential Geom. 91 (2012) 383-416 · 41 pages; published version

arxiv created 2012/10/01 · arxiv updated 2012/10/02

Abstract

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.

Cited by

• A Serre type vanishing property of the twisted primitive cohomology
• F-harmonic 3-forms and the Type IIA flow on 6-dimensional symplectic Lie algebras

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