Symplectic Boundary Conditions and Cohomology

Li-Sheng Tseng University of California, Irvine Lihan Wang University of Connecticut

Symplectic Geometry mathscidoc:1711.34001

We introduce new boundary conditions for differential forms on symplectic manifolds with boundary. These boundary conditions, dependent on the symplectic structure, allows us to write down elliptic boundary value problems for both second-order and fourth-order symplectic Laplacians and establish Hodge theories for the cohomologies of primitive forms on manifolds with boundary. We further use these boundary conditions to define a relative version of the primitive cohomologies and to relate primitive cohomologies with Lefschetz maps on manifolds with boundary. As we show, these cohomologies of primitive forms can distinguish certain Kahler structures of Kahler manifolds with boundary.
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@inproceedings{li-shengsymplectic,
  title={Symplectic Boundary Conditions and Cohomology},
  author={Li-Sheng Tseng, and Lihan Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20171121055241307713856},
}
Li-Sheng Tseng, and Lihan Wang. Symplectic Boundary Conditions and Cohomology. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20171121055241307713856.
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