Symplectic geometry on symplectic knot spaces

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3 Scopus citations


Symplectic knot spaces are the spaces of symplectic subspaces in a symplectic manifold M. We introduce a symplectic structure and show that the structure can be also obtained by the symplectic quotient method. We explain the correspondence between coisotropic submanifolds in M and Lagrangians in the symplectic knot space. We also define an almost complex structure on the symplectic knot space, and study the correspondence between almost complex submanifolds in M and holomorphic curves in the symplectic knot space.

Original languageEnglish
Pages (from-to)17-31
Number of pages15
JournalNew York Journal of Mathematics
StatePublished - 2007


  • Almost complex submanifold
  • Coisotropic submanifold
  • Holomorphic curve
  • Lagrangian submanifold
  • Symplectic knot space
  • Symplectic reduction


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