Open Access
July 2012 Cohomology and Hodge Theory on Symplectic Manifolds: II
Li-Sheng Tseng, Shing-Tung Yau
J. Differential Geom. 91(3): 417-443 (July 2012). DOI: 10.4310/jdg/1349292671


We show that the exterior derivative operator on a symplectic manifold has a natural decomposition into two linear differential operators, analogous to the Dolbeault operators in complex geometry. These operators map primitive forms into primitive forms and therefore lead directly to the construction of primitive cohomologies on symplectic manifolds. Using these operators, we introduce new primitive cohomologies that are analogous to the Dolbeault cohomology in the complex theory. Interestingly, the finiteness of these primitive cohomologies follows directly from an elliptic complex. We calculate the known primitive cohomologies on a nilmanifold and show that their dimensions can vary with the class of the symplectic form.


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Li-Sheng Tseng. Shing-Tung Yau. "Cohomology and Hodge Theory on Symplectic Manifolds: II." J. Differential Geom. 91 (3) 417 - 443, July 2012.


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

zbMATH: 1275.53080
MathSciNet: MR2981844
Digital Object Identifier: 10.4310/jdg/1349292671

Rights: Copyright © 2012 Lehigh University

Vol.91 • No. 3 • July 2012
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