Journal of Differential Geometry

Cohomology and Hodge Theory on Symplectic Manifolds: I

Li-Sheng Tseng and Shing-Tung Yau

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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.

Article information

Source
J. Differential Geom., Volume 91, Number 3 (2012), 383-416.

Dates
First available in Project Euclid: 3 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1349292670

Digital Object Identifier
doi:10.4310/jdg/1349292670

Mathematical Reviews number (MathSciNet)
MR2981843

Zentralblatt MATH identifier
1275.53079

Citation

Tseng, Li-Sheng; Yau, Shing-Tung. Cohomology and Hodge Theory on Symplectic Manifolds: I. J. Differential Geom. 91 (2012), no. 3, 383--416. doi:10.4310/jdg/1349292670. https://projecteuclid.org/euclid.jdg/1349292670


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See also

  • See: Li-Sheng Tseng, Shing-Tung Yau. Cohomology and Hodge Theory on Symplectic Manifolds: II. J. Differential Geom., vol. 91, no. 3 (2012), p. 417-443.