Open Access
July 2012 Cohomology and Hodge Theory on Symplectic Manifolds: I
Li-Sheng Tseng, Shing-Tung Yau
J. Differential Geom. 91(3): 383-416 (July 2012). DOI: 10.4310/jdg/1349292670


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.


Download Citation

Li-Sheng Tseng. Shing-Tung Yau. "Cohomology and Hodge Theory on Symplectic Manifolds: I." J. Differential Geom. 91 (3) 383 - 416, July 2012.


Published: July 2012
First available in Project Euclid: 3 October 2012

zbMATH: 1275.53079
MathSciNet: MR2981843
Digital Object Identifier: 10.4310/jdg/1349292670

Rights: Copyright © 2012 Lehigh University

Vol.91 • No. 3 • July 2012
Back to Top