Cohomology and hodge theory on symplectic manifolds: i

Li-Sheng Tseng University of California Shing-Tung Yau Harvard University

Differential Geometry mathscidoc:1609.10275

Distinguished Paper Award in 2017

Journal of Differential Geometry, 91, (3), 383-416, 2012
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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@inproceedings{li-sheng2012cohomology,
  title={COHOMOLOGY AND HODGE THEORY ON SYMPLECTIC MANIFOLDS: I},
  author={Li-Sheng Tseng, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913230713455769937},
  booktitle={Journal of Differential Geometry},
  volume={91},
  number={3},
  pages={383-416},
  year={2012},
}
Li-Sheng Tseng, and Shing-Tung Yau. COHOMOLOGY AND HODGE THEORY ON SYMPLECTIC MANIFOLDS: I. 2012. Vol. 91. In Journal of Differential Geometry. pp.383-416. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913230713455769937.
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